Aliquot sequences starting on integer powers n^i

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

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

Current version

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
U148 (142)
Orange with name code : Open-End reserved sequence calculated up to 10^120, 148 digits and 142 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 up to 10^120, 121 digits and 116 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 about n: Unnecessary to include for example n=8 or n=4 because they are powers of 2 already done.

Contributors

Type Entries
Primes 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47
Others: 79, 439, 82589933, (10^10+19)
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,
Perfect 6, 28, 496, 8128, 33550336, 8589869056
Cycles 220, 284
Others 10, 12, 14, 15, 20, 21, 22, 24, 26, 33, 34, 35, 42, 385, 770, 1155

Links and statistics

Links to pages
Choose type of sequences
Base & Link Decomposition All Primes Primes % Cycles Cycles % Opens Opens % Merges Merges %
2 2 559 556 99.46% 3 0.54% 0 0.00% 0 0.00%
3 3 335 176 52.54% 1 0.30% 158 47.16% 8 2.39%
5 5 250 114 45.60% 2 0.80% 134 53.60% 6 2.40%
6 2 * 3 206 99 48.06% 2 0.97% 105 50.97% 3 1.46%
7 7 189 97 51.32% 2 1.06% 90 47.62% 4 2.12%
10 2 * 5 160 80 50.00% 1 0.62% 79 49.38% 6 3.75%
11 11 153 83 54.25% 1 0.65% 69 45.10% 3 1.96%
12 2^2 * 3 148 71 47.97% 1 0.68% 76 51.35% 6 4.05%
13 13 145 81 55.86% 0 0.00% 64 44.14% 3 2.07%
14 2 * 7 140 76 54.29% 0 0.00% 64 45.71% 3 2.14%
15 3 * 5 140 66 47.14% 1 0.71% 73 52.14% 7 5.00%
17 17 140 67 47.86% 0 0.00% 73 52.14% 2 1.43%
18 2 * 3^2 140 129 92.14% 0 0.00% 11 7.86% 0 0.00%
19 19 140 66 47.14% 0 0.00% 74 52.86% 1 0.71%
20 2^2 * 5 100 56 56.00% 0 0.00% 44 44.00% 3 3.00%
21 3 * 7 100 55 55.00% 0 0.00% 45 45.00% 1 1.00%
22 2 * 11 100 55 55.00% 1 1.00% 44 44.00% 3 3.00%
23 23 1 2 3 4 5 6 7 8 9
24 2^3 * 3 1 2 3 4 5 6 7 8 9
26 2 * 13 1 2 3 4 5 6 7 8 9
28 2^2 * 7 1 2 3 4 5 6 7 8 9
29 29 1 2 3 4 5 6 7 8 9
30 2 * 3 * 5 1 2 3 4 5 6 7 8 9
162 2 * 3^4 72 71 98.61% 1 1.39% 0 0.00% 0 0.00%
220 2^2 * 5 * 11 1 2 3 4 5 6 7 8 9
284 2^2 * 71 1 2 3 4 5 6 7 8 9
2310 2 * 3 * 5 * 7 * 11 1 2 3 4 5 6 7 8 9
Total: 27 - 27 11 45.66% 59 4.55% 888 33.33% 99 15.15%
Total: 25 - 25 11 45.66% 59 4.55% 888 33.33% 99 15.15%
Total: 10 - 10 11 45.66% 59 4.55% 888 33.33% 99 15.15%
Total: 4 - 4 11 45.66% 59 4.55% 888 33.33% 99 15.15%
Total: 3 - 3 11 45.66% 59 4.55% 888 33.33% 99 15.15%
Total: 2 - 2 11 45.66% 59 4.55% 888 33.33% 99 15.15%
Total: 2 - 2 1 50.00% 1 1.55% 2 33.33% 55 55.55%
Total: 9 - 9 11 45.66% 59 4.55% 888 33.33% 99 15.15%

Statistics about all the bases

Total number of sequences:

Total number of sequences that end with a prime:

Total number of cycles:

Total number of open sequences:

Total number of merge sequences:

The base includes all integers exhaustively up to: 37 today