Aliquot sequences starting on integer powers n^i

Search and page maintained by Jean-Luc Garambois
Page designed by Karsten Bonath, 2018-2021

Aliquot sequences starting on integer powers n^i (for Open-End sequences, size of terms up to 10^120)

Reservation page, page summarizing the progress of calculations

Web site of this page: www.aliquotes.com
Origin and storage of data: FactorDB

Reservations

Base Reservations for Tables Being Initialized (* Bases ready to be added to the page):
179 (GAR), 181 (GAR), 227 (RFD), 229 (RFD), 1210 (GAR), 1184 (GAR), 31704 (GAR), 1264460 (GAR)

Reservations of sequences for further calculations after initialisation:
See explanations below in the "Definitions" section.

Reservations for matched parity (and doubled square) sequences, term <145 digits:
See the booking page for matched parity sequences.

Definitions

SymbolExplanation
A"A" or "GAR" for example is the code (see next table) of the one who has booked or calculated the aliquot sequence
A 7
P5
Green : aliquot sequence arrived at a 5 digits prime number after 7 iterations, calculations made by Anonymous
GAR 29
C1
Blue : aliquot sequence arrived on a cycle (here on a perfect number, but "C2" would have meant on an amicable number) after 29 iterations, calculations made by Garambois
GAR 2
U135 (134)
Orange with name code : Open-End reserved sequence and calculated with terms between 120 and 139 digits, 135 digits and 134 digits for the cofactor in this example, calculations made by Garambois. Blocked for reservation.
134
U121 (116)
Orange without name code : Open-End sequence not reserved and calculated with terms between 120 and 139 digits, 121 digits and 116 digits for the cofactor in this example. Free for reservation.
GAR 255
U145 (135)
Pink with name code : Open-End sequence reserved and calculated with terms above 140 digits, 145 digits and 135 digits for the cofactor in this example. Blocked for reservation.
255
U145 (135)
Pink without name code : Open-End sequence not reserved and calculated with terms above 140 digits, 145 digits and 135 digits for the cofactor in this example. Free for reservation.
134
U121 (116)
Yellow background of sequence: this sequence merges with given one as tooltip. Check the blue page of the main project to see if this sequence is Free for reservation.
107
U84 (82)
Colorless cells without name code : aliquot sequence not yet calculated or reserved. Free for reservation.
GAR 2
U117 (110)
Colorless cells with name code : aliquot sequence not yet calculated but reserved. Blocked for reservation.
Note: Unnecessary to include for example n=8 or n=4 because they are powers of 2 already done.

Contributors

AbbreviationName
AAnonymous
GARJean-Luc Garambois
LRVLaurV
KRBKarsten Bonath
RFDRichD
WPOWpolly
SWTSweety439
MBTMisterBitcoin
RCHRichs
GDBGd_barnes
HPPHappy5214
VBCVBCurtis
FRJFirejuggler
PFPPFPoitras
EDHEdwin Hall
UNCUnconnected
YOYYoyo
SERSergiosi
BURbur
NESNescro
HRZhenryzz
OKROliver Kruse
LUMLuminescence
BIRbirtwistlecaleb
ALFAlfred
SG1Stargate38
Type Entries
Primes 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173,
Others: 191, 193, 197, 199, 211, 223, 439, 8191, 82589933, 10000000019
Primorials 2, 6, 30, 210, 2310, 30030, 510510, 9699690, 223092870, 6469693230, 200560490130, 7420738134810
Doubles of squares 2, 18, 50, 72, 98, 162, 200, 242, 288, 338, 392, 450, 578, 648, 722, 800, 882, 968, 1058, 1152, 1250
Perfect 6, 28, 496, 8128, 33550336, 8589869056
Cycles (220, 284), (12496, 14288, 15472, 14536, 14264), (14316, 19116, ...)
Others 10, 12, 14, 15, 20, 21, 22, 24, 26, 33, 34, 35, 38, 39, 40, 42, 44, 45, 46, 48, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 65, 66, 68, 69, 70, 74, 75, 76, 77, 78, 80, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 99, 105, 119, 231, 276, 385, 552, 564, 660, 720, 966, 770, 1155, 15015

Links and statistics

The base includes all integers exhaustively up to: 101 today

Choose type of sequences

Base & Link Decomposition All Primes Primes % Cycles Cycles % Opens Opens % Merges Merges % Update
2 2 559 556 99.46% 3 0.54% 0 0.00% 0 0.00% 2022-02-17
3 3 335 186 55.52% 1 0.30% 148 44.18% 8 2.39% 2022-04-15
5 5 250 129 51.60% 2 0.80% 119 47.60% 6 2.40% 2022-06-12
6 2 * 3 210 111 52.86% 2 0.95% 97 46.19% 3 1.43% 2022-06-06
7 7 190 105 55.26% 2 1.05% 83 43.68% 4 2.11% 2022-05-01
10 2 * 5 160 85 53.12% 1 0.62% 74 46.25% 7 4.38% 2022-06-06
11 11 160 87 54.37% 1 0.62% 72 45.00% 3 1.88% 2022-05-15
12 2^2 * 3 150 77 51.33% 1 0.67% 72 48.00% 6 4.00% 2022-05-22
13 13 145 81 55.86% 0 0.00% 64 44.14% 3 2.07% 2022-03-12
14 2 * 7 140 81 57.86% 0 0.00% 59 42.14% 3 2.14% 2022-06-06
15 3 * 5 140 71 50.71% 1 0.71% 68 48.57% 7 5.00% 2022-05-15
17 17 140 73 52.14% 0 0.00% 67 47.86% 2 1.43% 2022-04-12
18 2 * 3^2 140 131 93.57% 0 0.00% 9 6.43% 0 0.00% 2022-05-08
19 19 140 72 51.43% 0 0.00% 68 48.57% 1 0.71% 2022-05-22
20 2^2 * 5 125 56 44.80% 0 0.00% 69 55.20% 3 2.40% 2022-06-22
21 3 * 7 125 56 44.80% 0 0.00% 69 55.20% 1 0.80% 2022-06-22
22 2 * 11 125 57 45.60% 1 0.80% 67 53.60% 3 2.40% 2022-06-22
23 23 125 56 44.80% 1 0.80% 68 54.40% 2 1.60% 2022-06-22
24 2^3 * 3 125 57 45.60% 0 0.00% 68 54.40% 3 2.40% 2022-06-22
26 2 * 13 120 59 49.17% 0 0.00% 61 50.83% 3 2.50% 2022-06-22
28 2^2 * 7 120 60 50.00% 1 0.83% 59 49.17% 1 0.83% 2022-06-22
29 29 120 58 48.33% 0 0.00% 62 51.67% 2 1.67% 2022-06-22
30 2 * 3 * 5 120 54 45.00% 0 0.00% 66 55.00% 1 0.83% 2022-06-22
31 31 110 55 50.00% 0 0.00% 55 50.00% 3 2.73% 2022-06-22
33 3 * 11 110 54 49.09% 0 0.00% 56 50.91% 3 2.73% 2022-06-22
34 2 * 17 110 58 52.73% 0 0.00% 52 47.27% 1 0.91% 2022-06-22
35 5 * 7 110 57 51.82% 0 0.00% 53 48.18% 2 1.82% 2022-06-22
37 37 110 57 51.82% 0 0.00% 53 48.18% 6 5.45% 2022-06-22
38 2 * 19 110 56 50.91% 1 0.91% 53 48.18% 3 2.73% 2022-06-22
39 3 * 13 110 51 46.36% 0 0.00% 59 53.64% 2 1.82% 2022-06-22
40 2^3 * 5 110 55 50.00% 0 0.00% 55 50.00% 1 0.91% 2022-06-22
41 41 100 51 51.00% 0 0.00% 49 49.00% 2 2.00% 2022-04-15
42 2 * 3 * 7 100 50 50.00% 0 0.00% 50 50.00% 3 3.00% 2022-05-08
43 43 100 54 54.00% 0 0.00% 46 46.00% 3 3.00% 2022-05-01
44 2^2 * 11 100 51 51.00% 0 0.00% 49 49.00% 3 3.00% 2022-05-15
45 3^2 * 5 100 57 57.00% 1 1.00% 42 42.00% 3 3.00% 2022-06-06
46 2 * 23 100 50 50.00% 0 0.00% 50 50.00% 4 4.00% 2022-05-29
47 47 100 54 54.00% 0 0.00% 46 46.00% 3 3.00% 2022-06-06
48 2^4 * 3 100 49 49.00% 0 0.00% 51 51.00% 2 2.00% 2022-05-01
50 2 * 5^2 100 100 100.00% 0 0.00% 0 0.00% 0 0.00% 2022-05-01
51 3 * 17 100 50 50.00% 0 0.00% 50 50.00% 2 2.00% 2022-06-12
52 2^2 * 13 100 50 50.00% 1 1.00% 49 49.00% 3 3.00% 2022-05-15
53 53 100 53 53.00% 1 1.00% 46 46.00% 2 2.00% 2022-06-06
54 2 * 3^3 100 48 48.00% 0 0.00% 52 52.00% 3 3.00% 2022-05-08
55 5 * 11 100 48 48.00% 0 0.00% 52 52.00% 2 2.00% 2022-05-08
56 2^3 * 7 100 48 48.00% 1 1.00% 51 51.00% 1 1.00% 2022-06-12
57 3 * 19 100 46 46.00% 1 1.00% 53 53.00% 1 1.00% 2022-06-06
58 2 * 29 100 47 47.00% 1 1.00% 52 52.00% 4 4.00% 2022-03-12
59 59 100 50 50.00% 0 0.00% 50 50.00% 3 3.00% 2022-05-29
60 2^2 * 3 * 5 100 49 49.00% 0 0.00% 51 51.00% 0 0.00% 2022-06-12
61 61 100 46 46.00% 0 0.00% 54 54.00% 5 5.00% 2022-05-08
62 2 * 31 100 49 49.00% 0 0.00% 51 51.00% 2 2.00% 2022-05-15
63 3^2 * 7 100 46 46.00% 1 1.00% 53 53.00% 1 1.00% 2022-05-01
65 5 * 13 100 48 48.00% 0 0.00% 52 52.00% 2 2.00% 2022-03-12
66 2 * 3 * 11 100 49 49.00% 0 0.00% 51 51.00% 3 3.00% 2022-05-15
67 67 100 46 46.00% 0 0.00% 54 54.00% 1 1.00% 2022-05-01
68 2^2 * 17 100 44 44.00% 0 0.00% 56 56.00% 3 3.00% 2022-05-08
69 3 * 23 100 46 46.00% 0 0.00% 54 54.00% 0 0.00% 2022-05-15
70 2 * 5 * 7 100 55 55.00% 0 0.00% 45 45.00% 5 5.00% 2022-03-12
71 71 100 56 56.00% 0 0.00% 44 44.00% 1 1.00% 2022-03-12
72 2^3 * 3^2 100 89 89.00% 0 0.00% 11 11.00% 0 0.00% 2022-05-08
73 73 100 56 56.00% 0 0.00% 44 44.00% 1 1.00% 2022-03-12
74 2 * 37 100 49 49.00% 0 0.00% 51 51.00% 2 2.00% 2022-05-15
75 3 * 5^2 100 51 51.00% 0 0.00% 49 49.00% 1 1.00% 2022-06-06
76 2^2 * 19 100 42 42.00% 0 0.00% 58 58.00% 2 2.00% 2022-06-12
77 7 * 11 100 39 39.00% 1 1.00% 60 60.00% 1 1.00% 2022-06-12
78 2 * 3 * 13 100 43 43.00% 0 0.00% 57 57.00% 0 0.00% 2022-06-12
79 79 100 55 55.00% 0 0.00% 45 45.00% 1 1.00% 2022-03-12
80 2^4 * 5 100 42 42.00% 0 0.00% 58 58.00% 3 3.00% 2022-05-01
82 2 * 41 100 43 43.00% 0 0.00% 57 57.00% 3 3.00% 2022-05-22
83 83 100 44 44.00% 0 0.00% 56 56.00% 1 1.00% 2022-05-01
84 2^2 * 3 * 7 100 42 42.00% 1 1.00% 57 57.00% 2 2.00% 2022-05-29
85 5 * 17 100 41 41.00% 1 1.00% 58 58.00% 2 2.00% 2022-06-06
86 2 * 43 100 43 43.00% 1 1.00% 56 56.00% 2 2.00% 2022-06-06
87 3 * 29 100 43 43.00% 0 0.00% 57 57.00% 0 0.00% 2022-06-12
88 2^3 * 11 100 35 35.00% 1 1.00% 64 64.00% 4 4.00% 2022-06-12
89 89 100 44 44.00% 0 0.00% 56 56.00% 2 2.00% 2022-06-12
90 2 * 3^2 * 5 100 44 44.00% 0 0.00% 56 56.00% 0 0.00% 2022-06-12
91 7 * 13 100 41 41.00% 0 0.00% 59 59.00% 4 4.00% 2022-05-01
92 2^2 * 23 100 41 41.00% 1 1.00% 58 58.00% 1 1.00% 2022-05-08
93 3 * 31 100 42 42.00% 0 0.00% 58 58.00% 0 0.00% 2022-05-08
94 2 * 47 100 37 37.00% 0 0.00% 63 63.00% 3 3.00% 2022-06-12
95 5 * 19 100 39 39.00% 1 1.00% 60 60.00% 2 2.00% 2022-06-06
96 2^5 * 3 100 42 42.00% 0 0.00% 58 58.00% 1 1.00% 2022-05-08
97 97 100 45 45.00% 0 0.00% 55 55.00% 4 4.00% 2022-05-01
98 2 * 7^2 100 93 93.00% 0 0.00% 7 7.00% 0 0.00% 2022-03-16
99 3^2 * 11 100 42 42.00% 0 0.00% 58 58.00% 1 1.00% 2022-05-15
101 101 95 40 42.11% 0 0.00% 55 57.89% 1 1.05% 2022-05-01
103 103 95 44 46.32% 1 1.05% 50 52.63% 0 0.00% 2022-05-29
105 3 * 5 * 7 95 40 42.11% 0 0.00% 55 57.89% 2 2.11% 2022-06-11
107 107 95 36 37.89% 0 0.00% 59 62.11% 2 2.11% 2022-05-22
109 109 95 38 40.00% 0 0.00% 57 60.00% 1 1.05% 2022-06-12
113 113 95 39 41.05% 0 0.00% 56 58.95% 3 3.16% 2022-06-12
119 7 * 17 95 42 44.21% 1 1.05% 52 54.74% 0 0.00% 2022-05-29
127 127 95 42 44.21% 0 0.00% 53 55.79% 2 2.11% 2022-06-12
131 131 95 38 40.00% 0 0.00% 57 60.00% 3 3.16% 2022-06-12
137 137 95 37 38.95% 0 0.00% 58 61.05% 0 0.00% 2022-06-11
139 139 95 38 40.00% 1 1.05% 56 58.95% 2 2.11% 2022-06-12
149 149 90 37 41.11% 0 0.00% 53 58.89% 0 0.00% 2022-06-06
151 151 90 35 38.89% 1 1.11% 54 60.00% 2 2.22% 2022-06-06
157 157 90 36 40.00% 1 1.11% 53 58.89% 2 2.22% 2022-06-06
162 2 * 3^4 85 76 89.41% 1 1.18% 8 9.41% 0 0.00% 2022-05-15
163 163 90 39 43.33% 0 0.00% 51 56.67% 1 1.11% 2022-06-12
167 167 90 39 43.33% 1 1.11% 50 55.56% 2 2.22% 2022-06-12
173 173 90 39 43.33% 0 0.00% 51 56.67% 2 2.22% 2022-06-12
191 191 90 33 36.67% 0 0.00% 57 63.33% 2 2.22% 2022-06-12
193 193 90 36 40.00% 1 1.11% 53 58.89% 0 0.00% 2022-06-06
197 197 90 37 41.11% 0 0.00% 53 58.89% 0 0.00% 2022-06-06
199 199 90 33 36.67% 0 0.00% 57 63.33% 1 1.11% 2022-06-12
200 2^3 * 5^2 80 67 83.75% 1 1.25% 12 15.00% 0 0.00% 2022-06-12
210 2 * 3 * 5 * 7 80 31 38.75% 1 1.25% 48 60.00% 1 1.25% 2022-05-01
211 211 80 36 45.00% 2 2.50% 42 52.50% 3 3.75% 2022-05-01
220 2^2 * 5 * 11 80 37 46.25% 1 1.25% 42 52.50% 0 0.00% 2022-05-29
223 223 80 31 38.75% 1 1.25% 48 60.00% 0 0.00% 2022-06-22
231 3 * 7 * 11 80 35 43.75% 0 0.00% 45 56.25% 1 1.25% 2022-05-01
242 2 * 11^2 70 69 98.57% 1 1.43% 0 0.00% 0 0.00% 2022-03-13
276 2^2 * 3 * 23 70 32 45.71% 0 0.00% 38 54.29% 2 2.86% 2022-05-29
284 2^2 * 71 70 33 47.14% 1 1.43% 36 51.43% 1 1.43% 2022-05-08
288 2^5 * 3^2 65 61 93.85% 0 0.00% 4 6.15% 0 0.00% 2022-06-22
338 2 * 13^2 65 60 92.31% 0 0.00% 5 7.69% 0 0.00% 2022-06-22
385 5 * 7 * 11 65 34 52.31% 0 0.00% 31 47.69% 2 3.08% 2022-06-22
392 2^3 * 7^2 65 59 90.77% 1 1.54% 5 7.69% 0 0.00% 2022-06-22
439 439 60 33 55.00% 1 1.67% 26 43.33% 0 0.00% 2022-05-01
450 2 * 3^2 * 5^2 60 60 100.00% 0 0.00% 0 0.00% 0 0.00% 2022-03-13
496 2^4 * 31 60 32 53.33% 1 1.67% 27 45.00% 1 1.67% 2022-05-01
552 2^3 * 3 * 23 60 28 46.67% 0 0.00% 32 53.33% 1 1.67% 2022-05-01
564 2^2 * 3 * 47 60 29 48.33% 0 0.00% 31 51.67% 0 0.00% 2022-06-06
578 2 * 17^2 60 60 100.00% 0 0.00% 0 0.00% 0 0.00% 2022-03-13
648 2^3 * 3^4 60 54 90.00% 0 0.00% 6 10.00% 0 0.00% 2022-05-29
660 2^2 * 3 * 5 * 11 60 29 48.33% 0 0.00% 31 51.67% 0 0.00% 2022-06-06
720 2^4 * 3^2 * 5 60 29 48.33% 0 0.00% 31 51.67% 0 0.00% 2022-05-08
722 2 * 19^2 60 56 93.33% 0 0.00% 4 6.67% 0 0.00% 2022-03-13
770 2 * 5 * 7 * 11 60 28 46.67% 0 0.00% 32 53.33% 1 1.67% 2022-05-08
800 2^5 * 5^2 60 60 100.00% 0 0.00% 0 0.00% 0 0.00% 2022-03-13
882 2 * 3^2 * 7^2 60 49 81.67% 1 1.67% 10 16.67% 0 0.00% 2022-05-15
966 2 * 3 * 7 * 23 60 25 41.67% 1 1.67% 34 56.67% 2 3.33% 2022-05-29
968 2^3 * 11^2 60 60 100.00% 0 0.00% 0 0.00% 0 0.00% 2022-03-13
1058 2 * 23^2 55 49 89.09% 0 0.00% 6 10.91% 0 0.00% 2022-06-22
1152 2^7 * 3^2 55 43 78.18% 0 0.00% 12 21.82% 0 0.00% 2022-06-22
1155 3 * 5 * 7 * 11 55 26 47.27% 0 0.00% 29 52.73% 2 3.64% 2022-06-22
1250 2 * 5^4 55 45 81.82% 0 0.00% 10 18.18% 0 0.00% 2022-06-22
2310 2 * 3 * 5 * 7 * 11 50 24 48.00% 0 0.00% 26 52.00% 1 2.00% 2022-05-22
8128 2^6 * 127 40 21 52.50% 2 5.00% 17 42.50% 0 0.00% 2022-05-01
8191 8191 40 21 52.50% 0 0.00% 19 47.50% 1 2.50% 2022-06-12
12496 2^4 * 11 * 71 40 21 52.50% 1 2.50% 18 45.00% 0 0.00% 2022-06-06
14264 2^3 * 1783 40 18 45.00% 1 2.50% 21 52.50% 2 5.00% 2022-05-01
14288 2^4 * 19 * 47 40 20 50.00% 1 2.50% 19 47.50% 0 0.00% 2022-05-01
14316 2^2 * 3 * 1193 40 17 42.50% 2 5.00% 21 52.50% 0 0.00% 2022-05-22
14536 2^3 * 23 * 79 40 18 45.00% 1 2.50% 21 52.50% 1 2.50% 2022-04-15
15015 3 * 5 * 7 * 11 * 13 40 22 55.00% 0 0.00% 18 45.00% 0 0.00% 2022-05-01
15472 2^4 * 967 40 20 50.00% 3 7.50% 17 42.50% 1 2.50% 2022-05-29
19116 2^2 * 3^4 * 59 40 19 47.50% 1 2.50% 20 50.00% 0 0.00% 2022-05-01
30030 2 * 3 * 5 * 7 * 11 * 13 40 18 45.00% 0 0.00% 22 55.00% 2 5.00% 2022-05-29
510510 2 * 3 * 5 * 7 * 11 * 13 * 17 30 13 43.33% 0 0.00% 17 56.67% 1 3.33% 2022-03-13
9699690 2 * 3 * 5 * 7 * 11 * 13 * 17 * 19 25 10 40.00% 0 0.00% 15 60.00% 0 0.00% 2022-03-13
33550336 2^12 * 8191 25 10 40.00% 1 4.00% 14 56.00% 0 0.00% 2022-03-13
82589933 82589933 20 10 50.00% 0 0.00% 10 50.00% 0 0.00% 2022-03-13
223092870 2 * 3 * 5 * 7 * 11 * 13 * 17 * 19 * 23 20 9 45.00% 0 0.00% 11 55.00% 0 0.00% 2022-06-05
6469693230 2 * 3 * 5 * 7 * 11 * 13 * 17 * 19 * 23 * 29 20 8 40.00% 0 0.00% 12 60.00% 0 0.00% 2022-03-13
8589869056 2^16 * 131071 20 8 40.00% 1 5.00% 11 55.00% 0 0.00% 2022-03-13
10000000019 10000000019 15 9 60.00% 0 0.00% 6 40.00% 0 0.00% 2022-05-08
200560490130 2 * 3 * 5 * 7 * 11 * 13 * 17 * 19 * 23 * 29 * 31 14 6 42.86% 0 0.00% 8 57.14% 0 0.00% 2022-03-13
7420738134810 2 * 3 * 5 * 7 * 11 * 13 * 17 * 19 * 23 * 29 * 31 * 37 14 7 50.00% 0 0.00% 7 50.00% 1 7.14% 2022-03-13
Total: 163 - 15237 8141 53.43% 67 0.44% 7029 46.13% 258 1.69% -
Total: 162 - 14678 7585 51.68% 64 0.44% 7029 47.89% 258 1.76% -
Total: 50 - 5734 3025 52.76% 21 0.37% 2688 46.88% 99 1.73% -
Total: 12 - 1182 847 71.66% 6 0.51% 329 27.83% 10 0.85% -
Total: 21 - 2014 1897 94.19% 8 0.40% 109 5.41% 0 0.00% -
Total: 6 - 475 242 50.95% 8 1.68% 225 47.37% 5 1.05% -
Total: 9 - 430 203 47.21% 12 2.79% 215 50.00% 5 1.16% -
Total: 68 - 6730 3150 46.81% 20 0.30% 3560 52.90% 142 2.11% -