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

Author

Zoltan Galantai, Jan 23 2023

Keywords

• nonn
• more

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

• 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.