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

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

Offset

1,5

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

Table of n, a(n) for n=1..20.

Sergei Chernykh, Amicable pairs list

Zoltan Galantai, Number of odd amicable pairs where the smaller term of the pair is less than 10^20

Crossrefs

Cf. A066873, A259180, A262623, A262622, A262625, A005408.

Sequence in context: A278613 A072632 A001671 * A309226 A278616 A278615

Adjacent sequences: A360051 A360052 A360053 * A360055 A360056 A360057

Keyword

nonn,more

Author

Zoltan Galantai, Jan 23 2023

Status

approved