cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A262623 Amicable pairs of odd numbers.

Original entry on oeis.org

12285, 14595, 67095, 71145, 69615, 87633, 100485, 124155, 122265, 139815, 522405, 525915, 802725, 863835, 947835, 1125765, 1175265, 1438983, 1280565, 1340235, 1358595, 1486845, 1798875, 1870245, 4482765, 5120595, 5357625, 5684679, 5730615, 6088905, 6377175, 6680025, 8619765, 9627915, 9071685, 9498555, 9206925, 10791795
Offset: 1

Views

Author

Omar E. Pol, Nov 09 2015

Keywords

Comments

If there are no amicable pairs whose members have distinct parity then this is also the odd terms of A259180.
First differs from A262625 at a(4).

References

  • Song Y. Yan, Perfect, Amicable and Sociable Numbers. A Computational Approach, World Scientific, 1996, pages 151 - 153.

Links

Crossrefs

Cf. A002025, A002046, A005408, A063990, A259180, A262622, A262625.

Programs

  • PARI
    lista(nn) = {forstep(n=1, nn, 2, m = sigma(n)-n; if ((m > n) && (n==sigma(m)-m), print1(n, ", ", m, ", ")););} \\ Michel Marcus, Nov 14 2015

A328256 Amicable pairs of cyclops numbers.

Original entry on oeis.org

1280565, 1340235, 71526069316, 75257076284, 1453520375775, 1561230417825, 1568650892445, 1995690781539, 2714480497936, 2854320218864, 5776910172896, 5864460215584, 5818350517628, 6516910297732, 6111770382135, 6139270339785, 9176850735616, 9194440569344, 114552504952875, 123277906567125
Offset: 1

Views

Author

Omar E. Pol, Oct 09 2019

Keywords

Comments

Amicable pairs (A259180) where both members are cyclops numbers (A134808).
Is this sequence finite? What is the largest known pair?
Up to 2^64 there are 439 pairs, the largest of them is {9591988390446931328, 9596251990981497472} (Eldar).

Examples

			{1280565, 1340235} is the first amicable pair where both members are cyclops numbers, so a(1) = 1280565 and a(2) = 1340235.

Links

Crossrefs

Subsequence of A259180.
Cf. A002025, A002046, A134808, A262622, A262623.

Extensions

More terms from Amiram Eldar, Oct 09 2019

A360054 Number of odd amicable pairs where the smaller term of the pair is less than 10^n.

Original entry on oeis.org

0, 0, 0, 0, 3, 8, 21, 55, 154, 412, 1088, 2632, 6532, 15371, 35218, 79982, 180061, 402560, 894404, 1975742
Offset: 1

Views

Author

Zoltan Galantai, Jan 23 2023

Keywords

Comments

The list starts with n=1.
Comparing with the numbers of even amicable pairs in A066873, up to 10^4, the proportion of odd amicable pairs is 0%; up to 10^5 it is 23% and up to 10^10 is 28.9%. Up to 10^15, it is 40.4% and up to 10^19 this percentage is 45.9%. It is possible that this trend holds true for more amicable pairs, and thus most amicable number pairs are odd.

References

  • Song Y. Yan, Perfect, Amicable and Sociable Numbers. A Computational Approach, World Scientific, 1996, pages 151 - 153.

Links

Crossrefs

Cf. A066873, A259180, A262623, A262622, A262625, A005408.
Showing 1-3 of 3 results.

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