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

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

Data table for n = 2 = 2
Stats: All: 559 /  Done: 549 ➔ 98.21%  /  Open:  7 ( 7) ➔ 1.25%  /  Merges:  0 ➔ 0.00%  /  Cycle:  3 ➔ 0.54% 

Data table for n = 3 = 3
Stats: All: 335 /  Done: 171 ➔ 51.04%  /  Open: 164 (156) ➔ 48.96%  /  Merges:  8 ➔ 2.39%  /  Cycle:  0 ➔ 0.00% 

Data table for n = 5 = 5
Stats: All: 250 /  Done: 114 ➔ 45.60%  /  Open: 134 (130) ➔ 53.60%  /  Merges:  6 ➔ 2.40%  /  Cycle:  2 ➔ 0.80% 

Data table for n = 6 = 2 * 3
Stats: All: 206 /  Done:  99 ➔ 48.06%  /  Open: 105 (102) ➔ 50.97%  /  Merges:  3 ➔ 1.46%  /  Cycle:  2 ➔ 0.97% 

Data table for n = 7 = 7
Stats: All: 189 /  Done:  97 ➔ 51.32%  /  Open:  90 ( 89) ➔ 47.62%  /  Merges:  4 ➔ 2.12%  /  Cycle:  2 ➔ 1.06% 

Data table for n = 10 = 2 * 5
Stats: All: 160 /  Done:  80 ➔ 50.00%  /  Open:  79 ( 75) ➔ 49.38%  /  Merges:  5 ➔ 3.12%  /  Cycle:  1 ➔ 0.62% 

Data table for n = 11 = 11
Stats: All: 153 /  Done:  83 ➔ 54.25%  /  Open:  69 ( 69) ➔ 45.10%  /  Merges:  3 ➔ 1.96%  /  Cycle:  1 ➔ 0.65% 

Data table for n = 12 = 2^2 * 3
Stats: All: 148 /  Done:  70 ➔ 47.30%  /  Open:  77 ( 77) ➔ 52.03%  /  Merges:  6 ➔ 4.05%  /  Cycle:  1 ➔ 0.68% 

Data table for n = 13 = 13
Stats: All: 143 /  Done:  78 ➔ 54.55%  /  Open:  65 ( 54) ➔ 45.45%  /  Merges:  3 ➔ 2.10%  /  Cycle:  0 ➔ 0.00% 

Data table for n = 14 = 2 * 7
Stats: All: 140 /  Done:  70 ➔ 50.00%  /  Open:  70 ( 67) ➔ 50.00%  /  Merges:  3 ➔ 2.14%  /  Cycle:  0 ➔ 0.00% 

Data table for n = 15 = 3 * 5
Stats: All: 139 /  Done:  62 ➔ 44.60%  /  Open:  76 ( 75) ➔ 54.68%  /  Merges:  6 ➔ 4.32%  /  Cycle:  1 ➔ 0.72% 

Data table for n = 17 = 17
Stats: All: 131 /  Done:  62 ➔ 47.33%  /  Open:  69 ( 65) ➔ 52.67%  /  Merges:  2 ➔ 1.53%  /  Cycle:  0 ➔ 0.00% 

Data table for n = 18 = 2 * 3^2
Stats: All: 129 /  Done: 129 ➔ 100.00%  /  Open:  0 ( 0) ➔ 0.00%  /  Merges:  0 ➔ 0.00%  /  Cycle:  0 ➔ 0.00% 

Data table for n = 19 = 19
Stats: All: 96 /  Done:  56 ➔ 58.33%  /  Open:  40 ( 9) ➔ 41.67%  /  Merges:  1 ➔ 1.04%  /  Cycle:  0 ➔ 0.00% 

Data table for n = 20 = 2^2 * 5
Stats: All: 92 /  Done:  51 ➔ 55.43%  /  Open:  41 ( 9) ➔ 44.57%  /  Merges:  3 ➔ 3.26%  /  Cycle:  0 ➔ 0.00% 

Data table for n = 21 = 3 * 7
Stats: All: 91 /  Done:  50 ➔ 54.95%  /  Open:  41 ( 38) ➔ 45.05%  /  Merges:  1 ➔ 1.10%  /  Cycle:  0 ➔ 0.00% 

Data table for n = 23 = 23
Stats: All: 89 /  Done:  48 ➔ 53.93%  /  Open:  40 ( 9) ➔ 44.94%  /  Merges:  2 ➔ 2.25%  /  Cycle:  1 ➔ 1.12% 

Data table for n = 24 = 2^3 * 3
Stats: All: 86 /  Done:  50 ➔ 58.14%  /  Open:  36 ( 5) ➔ 41.86%  /  Merges:  2 ➔ 2.33%  /  Cycle:  0 ➔ 0.00% 

Data table for n = 28 = 2^2 * 7
Stats: All: 84 /  Done:  52 ➔ 61.90%  /  Open:  31 ( 31) ➔ 36.90%  /  Merges:  1 ➔ 1.19%  /  Cycle:  1 ➔ 1.19% 

Data table for n = 29 = 29
Stats: All: 83 /  Done:  47 ➔ 56.63%  /  Open:  36 ( 5) ➔ 43.37%  /  Merges:  2 ➔ 2.41%  /  Cycle:  0 ➔ 0.00% 

Data table for n = 30 = 2 * 3 * 5
Stats: All: 82 /  Done:  45 ➔ 54.88%  /  Open:  37 ( 26) ➔ 45.12%  /  Merges:  1 ➔ 1.22%  /  Cycle:  0 ➔ 0.00% 

Data table for n = 31 = 31
Stats: All: 83 /  Done:  47 ➔ 56.63%  /  Open:  36 ( 29) ➔ 43.37%  /  Merges:  2 ➔ 2.41%  /  Cycle:  0 ➔ 0.00% 

Data table for n = 50 = 2 * 5^2
Stats: All: 95 /  Done:  78 ➔ 82.11%  /  Open:  17 ( 17) ➔ 17.89%  /  Merges:  0 ➔ 0.00%  /  Cycle:  0 ➔ 0.00% 

Data table for n = 79 = 79
Stats: All: 63 /  Done:  35 ➔ 55.56%  /  Open:  28 ( 3) ➔ 44.44%  /  Merges:  0 ➔ 0.00%  /  Cycle:  0 ➔ 0.00% 

Data table for n = 98 = 2 * 7^2
Stats: All: 82 /  Done:  76 ➔ 92.68%  /  Open:  6 ( 6) ➔ 7.32%  /  Merges:  0 ➔ 0.00%  /  Cycle:  0 ➔ 0.00% 

Data table for n = 162 = 2 * 3^4
Stats: All: 72 /  Done:  53 ➔ 73.61%  /  Open:  18 ( 18) ➔ 25.00%  /  Merges:  0 ➔ 0.00%  /  Cycle:  1 ➔ 1.39% 

Data table for n = 210 = 2 * 3 * 5 * 7
Stats: All: 52 /  Done:  25 ➔ 48.08%  /  Open:  26 ( 3) ➔ 50.00%  /  Merges:  1 ➔ 1.92%  /  Cycle:  1 ➔ 1.92% 

Data table for n = 385 = 5 * 7 * 11
Stats: All: 49 /  Done:  29 ➔ 59.18%  /  Open:  20 ( 4) ➔ 40.82%  /  Merges:  2 ➔ 4.08%  /  Cycle:  0 ➔ 0.00% 

Data table for n = 439 = 439
Stats: All: 47 /  Done:  27 ➔ 57.45%  /  Open:  20 ( 16) ➔ 42.55%  /  Merges:  0 ➔ 0.00%  /  Cycle:  0 ➔ 0.00% 

Data table for n = 496 = 2^4 * 31
Stats: All: 44 /  Done:  24 ➔ 54.55%  /  Open:  19 ( 19) ➔ 43.18%  /  Merges:  1 ➔ 2.27%  /  Cycle:  1 ➔ 2.27% 

Data table for n = 770 = 2 * 5 * 7 * 11
Stats: All: 42 /  Done:  23 ➔ 54.76%  /  Open:  19 ( 19) ➔ 45.24%  /  Merges:  1 ➔ 2.38%  /  Cycle:  0 ➔ 0.00% 

Data table for n = 1155 = 3 * 5 * 7 *11
Stats: All: 41 /  Done:  22 ➔ 53.66%  /  Open:  19 ( 19) ➔ 46.34%  /  Merges:  2 ➔ 4.88%  /  Cycle:  0 ➔ 0.00% 

Data table for n = 2310 = 2 * 3 * 5 * 7 * 11
Stats: All: 35 /  Done:  18 ➔ 51.43%  /  Open:  17 ( 17) ➔ 48.57%  /  Merges:  1 ➔ 2.86%  /  Cycle:  0 ➔ 0.00% 

Data table for n = 8128 = 2^6 * 127
Stats: All: 30 /  Done:  16 ➔ 53.33%  /  Open:  12 ( 12) ➔ 40.00%  /  Merges:  0 ➔ 0.00%  /  Cycle:  2 ➔ 6.67% 

Data table for n = 30030 = 2 * 3 * 5 * 7 * 11 * 13
Stats: All: 26 /  Done:  14 ➔ 53.85%  /  Open:  12 ( 12) ➔ 46.15%  /  Merges:  2 ➔ 7.69%  /  Cycle:  0 ➔ 0.00% 

Data table for n = 510510 = 2 * 3 * 5 * 7 * 11 * 13 * 17
Stats: All: 22 /  Done:  12 ➔ 54.55%  /  Open:  10 ( 10) ➔ 45.45%  /  Merges:  1 ➔ 4.55%  /  Cycle:  0 ➔ 0.00% 

Data table for n = 9699690 = 2 * 3 * 5 * 7 * 11 * 13 * 17 * 19
Stats: All: 18 /  Done:  9 ➔ 50.00%  /  Open:  9 ( 9) ➔ 50.00%  /  Merges:  0 ➔ 0.00%  /  Cycle:  0 ➔ 0.00% 

Data table for n = 82589933 = 82589933
Stats: All: 17 /  Done:  9 ➔ 52.94%  /  Open:  8 ( 8) ➔ 47.06%  /  Merges:  0 ➔ 0.00%  /  Cycle:  0 ➔ 0.00% 

Data table for n = (10^10+19) = (10^10+19)
Stats: All: 15 /  Done:  9 ➔ 60.00%  /  Open:  6 ( 6) ➔ 40.00%  /  Merges:  0 ➔ 0.00%  /  Cycle:  0 ➔ 0.00%