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

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.
255
U145 (135)
Pink with or without name code : Open-End sequence reserved or 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
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
Type Entries
Primes 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53
Others: 79, 211, 439, 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
Others: 882
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, 62, 74, 75, 105, 231, 276, 385, 552, 564, 660, 720, 966, 770, 1155, 15015

Links and statistics

The base includes all integers exhaustively up to: 58 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% 2021-09-05
3 3 335 178 53.13% 1 0.30% 156 46.57% 8 2.39% 2021-09-05
5 5 250 115 46.00% 2 0.80% 133 53.20% 6 2.40% 2021-09-05
6 2 * 3 210 101 48.10% 2 0.95% 107 50.95% 3 1.43% 2021-09-05
7 7 190 99 52.11% 2 1.05% 89 46.84% 4 2.11% 2021-09-05
10 2 * 5 160 80 50.00% 1 0.62% 79 49.38% 7 4.38% 2021-09-05
11 11 160 85 53.12% 1 0.62% 74 46.25% 3 1.88% 2021-09-05
12 2^2 * 3 150 72 48.00% 1 0.67% 77 51.33% 6 4.00% 2021-09-05
13 13 145 81 55.86% 0 0.00% 64 44.14% 3 2.07% 2021-09-05
14 2 * 7 140 76 54.29% 0 0.00% 64 45.71% 3 2.14% 2021-09-05
15 3 * 5 140 66 47.14% 1 0.71% 73 52.14% 7 5.00% 2021-09-05
17 17 140 67 47.86% 0 0.00% 73 52.14% 2 1.43% 2021-09-05
18 2 * 3^2 140 129 92.14% 0 0.00% 11 7.86% 0 0.00% 2021-09-05
19 19 140 66 47.14% 0 0.00% 74 52.86% 1 0.71% 2021-09-05
20 2^2 * 5 100 56 56.00% 0 0.00% 44 44.00% 3 3.00% 2021-09-05
21 3 * 7 100 56 56.00% 0 0.00% 44 44.00% 1 1.00% 2021-09-05
22 2 * 11 100 57 57.00% 1 1.00% 42 42.00% 3 3.00% 2021-09-05
23 23 100 53 53.00% 1 1.00% 46 46.00% 2 2.00% 2021-09-05
24 2^3 * 3 100 57 57.00% 0 0.00% 43 43.00% 3 3.00% 2021-09-05
26 2 * 13 100 59 59.00% 0 0.00% 41 41.00% 3 3.00% 2021-09-05
28 2^2 * 7 100 52 52.00% 1 1.00% 47 47.00% 1 1.00% 2021-09-05
29 29 100 56 56.00% 0 0.00% 44 44.00% 2 2.00% 2021-09-05
30 2 * 3 * 5 100 53 53.00% 0 0.00% 47 47.00% 1 1.00% 2021-09-05
31 31 100 54 54.00% 0 0.00% 46 46.00% 3 3.00% 2021-09-05
33 3 * 11 100 52 52.00% 0 0.00% 48 48.00% 3 3.00% 2021-09-05
34 2 * 17 100 54 54.00% 0 0.00% 46 46.00% 1 1.00% 2021-09-05
35 5 * 7 100 55 55.00% 0 0.00% 45 45.00% 2 2.00% 2021-09-05
37 37 100 56 56.00% 0 0.00% 44 44.00% 6 6.00% 2021-09-05
38 2 * 19 100 52 52.00% 1 1.00% 47 47.00% 3 3.00% 2021-09-05
39 3 * 13 100 48 48.00% 0 0.00% 52 52.00% 2 2.00% 2021-09-05
40 2^3 * 5 100 53 53.00% 0 0.00% 47 47.00% 1 1.00% 2021-09-05
41 41 100 49 49.00% 0 0.00% 51 51.00% 2 2.00% 2021-09-05
42 2 * 3 * 7 100 49 49.00% 0 0.00% 51 51.00% 3 3.00% 2021-09-05
43 43 100 53 53.00% 0 0.00% 47 47.00% 3 3.00% 2021-09-05
44 2^2 * 11 100 48 48.00% 0 0.00% 52 52.00% 3 3.00% 2021-09-05
45 3^2 * 5 100 54 54.00% 1 1.00% 45 45.00% 3 3.00% 2021-09-05
46 2 * 23 100 47 47.00% 0 0.00% 53 53.00% 4 4.00% 2021-09-05
47 47 100 51 51.00% 0 0.00% 49 49.00% 3 3.00% 2021-09-05
48 2^4 * 3 100 47 47.00% 0 0.00% 53 53.00% 2 2.00% 2021-09-05
50 2 * 5^2 100 98 98.00% 0 0.00% 2 2.00% 0 0.00% 2021-09-05
51 3 * 17 100 43 43.00% 0 0.00% 57 57.00% 2 2.00% 2021-09-05
52 2^2 * 13 100 43 43.00% 0 0.00% 57 57.00% 3 3.00% 2021-09-05
53 53 100 52 52.00% 1 1.00% 47 47.00% 2 2.00% 2021-09-05
54 2 * 3^3 100 40 40.00% 0 0.00% 60 60.00% 3 3.00% 2021-09-05
55 5 * 11 100 41 41.00% 0 0.00% 59 59.00% 2 2.00% 2021-09-05
56 2^3 * 7 100 40 40.00% 1 1.00% 59 59.00% 1 1.00% 2021-09-05
57 3 * 19 100 37 37.00% 1 1.00% 62 62.00% 1 1.00% 2021-09-05
58 2 * 29 100 45 45.00% 1 1.00% 54 54.00% 4 4.00% 2021-09-05
62 2 * 31 100 46 46.00% 0 0.00% 54 54.00% 2 2.00% 2021-09-05
72 2^3 * 3^2 100 88 88.00% 0 0.00% 12 12.00% 0 0.00% 2021-09-05
74 2 * 37 100 45 45.00% 0 0.00% 55 55.00% 2 2.00% 2021-09-05
75 3 * 5^2 100 47 47.00% 0 0.00% 53 53.00% 1 1.00% 2021-09-05
79 79 100 51 51.00% 0 0.00% 49 49.00% 1 1.00% 2021-09-05
98 2 * 7^2 100 82 82.00% 0 0.00% 18 18.00% 0 0.00% 2021-09-05
105 3 * 5 * 7 90 38 42.22% 0 0.00% 52 57.78% 2 2.22% 2021-09-05
162 2 * 3^4 80 76 95.00% 1 1.25% 3 3.75% 0 0.00% 2021-09-05
200 2^3 * 5^2 80 62 77.50% 1 1.25% 17 21.25% 0 0.00% 2021-09-05
210 2 * 3 * 5 * 7 80 29 36.25% 1 1.25% 50 62.50% 1 1.25% 2021-09-05
211 211 80 32 40.00% 2 2.50% 46 57.50% 3 3.75% 2021-09-05
220 2^2 * 5 * 11 80 35 43.75% 1 1.25% 44 55.00% 0 0.00% 2021-09-05
231 3 * 7 * 11 80 33 41.25% 0 0.00% 47 58.75% 1 1.25% 2021-09-05
242 2 * 11^2 70 69 98.57% 1 1.43% 0 0.00% 0 0.00% 2021-09-05
276 2^2 * 3 * 23 70 28 40.00% 0 0.00% 42 60.00% 2 2.86% 2021-09-05
284 2^2 * 71 70 31 44.29% 1 1.43% 38 54.29% 1 1.43% 2021-09-05
288 2^5 * 3^2 60 60 100.00% 0 0.00% 0 0.00% 0 0.00% 2021-09-05
338 2 * 13^2 60 60 100.00% 0 0.00% 0 0.00% 0 0.00% 2021-09-05
385 5 * 7 * 11 60 34 56.67% 0 0.00% 26 43.33% 2 3.33% 2021-09-05
392 2^3 * 7^2 60 59 98.33% 1 1.67% 0 0.00% 0 0.00% 2021-09-05
439 439 60 31 51.67% 1 1.67% 28 46.67% 0 0.00% 2021-09-05
450 2 * 3^2 * 5^2 60 60 100.00% 0 0.00% 0 0.00% 0 0.00% 2021-09-05
496 2^4 * 31 60 31 51.67% 1 1.67% 28 46.67% 1 1.67% 2021-09-05
552 2^3 * 3 * 23 60 25 41.67% 0 0.00% 35 58.33% 1 1.67% 2021-09-05
564 2^2 * 3 * 47 60 25 41.67% 0 0.00% 35 58.33% 0 0.00% 2021-09-05
578 2 * 17^2 60 60 100.00% 0 0.00% 0 0.00% 0 0.00% 2021-09-05
648 2^3 * 3^4 60 50 83.33% 0 0.00% 10 16.67% 0 0.00% 2021-09-05
660 2^2 * 3 * 5 * 11 60 19 31.67% 0 0.00% 41 68.33% 1 1.67% 2021-09-05
720 2^4 * 3^2 * 5 60 22 36.67% 0 0.00% 38 63.33% 0 0.00% 2021-09-05
722 2 * 19^2 60 56 93.33% 0 0.00% 4 6.67% 0 0.00% 2021-09-05
770 2 * 5 * 7 * 11 60 27 45.00% 0 0.00% 33 55.00% 1 1.67% 2021-09-05
882 2 * 3^2 * 7^2 60 44 73.33% 1 1.67% 15 25.00% 0 0.00% 2021-09-05
966 2 * 3 * 7 * 23 60 22 36.67% 1 1.67% 37 61.67% 2 3.33% 2021-09-05
1155 3 * 5 * 7 * 11 50 25 50.00% 0 0.00% 25 50.00% 2 4.00% 2021-09-05
2310 2 * 3 * 5 * 7 * 11 50 22 44.00% 0 0.00% 28 56.00% 1 2.00% 2021-09-05
8128 2^6 * 127 40 20 50.00% 2 5.00% 18 45.00% 0 0.00% 2021-09-05
12496 2^4 * 11 * 71 40 18 45.00% 1 2.50% 21 52.50% 0 0.00% 2021-09-05
14288 2^4 * 19 * 47 40 19 47.50% 1 2.50% 20 50.00% 0 0.00% 2021-09-05
14316 2^2 * 3 * 1193 40 15 37.50% 2 5.00% 23 57.50% 0 0.00% 2021-09-05
14264 2^3 * 1783 40 16 40.00% 1 2.50% 23 57.50% 2 5.00% 2021-09-05
14536 2^3 * 23 * 79 40 17 42.50% 1 2.50% 22 55.00% 1 2.50% 2021-09-05
15472 2^4 * 967 40 17 42.50% 3 7.50% 20 50.00% 1 2.50% 2021-09-05
15015 3 * 5 * 7 * 11 * 13 40 20 50.00% 0 0.00% 20 50.00% 0 0.00% 2021-09-05
19116 2^2 * 3^4 * 59 40 17 42.50% 1 2.50% 22 55.00% 0 0.00% 2021-09-05
30030 2 * 3 * 5 * 7 * 11 * 13 40 17 42.50% 0 0.00% 23 57.50% 2 5.00% 2021-09-05
510510 2 * 3 * 5 * 7 * 11 * 13 * 17 30 13 43.33% 0 0.00% 17 56.67% 1 3.33% 2021-09-05
9699690 2 * 3 * 5 * 7 * 11 * 13 * 17 * 19 25 10 40.00% 0 0.00% 15 60.00% 0 0.00% 2021-09-05
33550336 2^12 * 8191 25 10 40.00% 1 4.00% 14 56.00% 0 0.00% 2021-09-05
82589933 82589933 20 10 50.00% 0 0.00% 10 50.00% 0 0.00% 2021-09-05
223092870 2 * 3 * 5 * 7 * 11 * 13 * 17 * 19 * 23 20 9 45.00% 0 0.00% 11 55.00% 0 0.00% 2021-09-05
6469693230 2 * 3 * 5 * 7 * 11 * 13 * 17 * 19 * 23 * 29 20 8 40.00% 0 0.00% 12 60.00% 0 0.00% 2021-09-05
8589869056 2^16 * 131071 20 8 40.00% 1 5.00% 11 55.00% 0 0.00% 2021-09-05
10000000019 10000000019 15 9 60.00% 0 0.00% 6 40.00% 0 0.00% 2021-09-05
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% 2021-09-05
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% 2021-09-05
Total: 103 - 9362 5321 56.84% 50 0.53% 3991 42.63% 169 1.81% -
Total: 102 - 8803 4765 54.13% 47 0.53% 3991 45.34% 169 1.92% -
Total: 21 - 2994 1804 60.25% 14 0.47% 1176 39.28% 54 1.80% -
Total: 12 - 1162 831 71.51% 6 0.52% 325 27.97% 10 0.86% -
Total: 16 - 1709 1609 94.15% 8 0.47% 92 5.38% 0 0.00% -
Total: 6 - 455 222 48.79% 8 1.76% 225 49.45% 5 1.10% -
Total: 9 - 430 185 43.02% 12 2.79% 233 54.19% 5 1.16% -
Total: 42 - 3940 1883 47.79% 10 0.25% 2047 51.95% 98 2.49% -