A215491 Smaller members of regular amicable pairs.

220, 2620, 5020, 10744, 17296, 63020, 66928, 67095, 69615, 100485, 122265, 142310, 171856, 176272, 185368, 196724, 308620, 356408, 437456, 503056, 522405, 600392, 609928, 624184, 635624, 643336, 667964, 726104, 898216, 947835, 998104, 1077890, 1154450

Offset

1,1

Comments

An amicable pair (M,K) = (g*m, g*k) with g = gcd(M,K) is called regular if m and k are squarefree, and gcd(g,m) = gcd(g,k) = 1. Otherwise it is called irregular.

A regular amicable pair (M, K) has the property A048250(M) = A048250(K). - Jonathan Pappas, Jan 30 2022

Out of the 415442 amicable pairs below 10^17, exactly 330435 of them are regular (79.5%). The ratio appears to slowly increase. - Jonathan Pappas, Jan 31 2022

Links

Michel Marcus and Jonathan Pappas, Table of n, a(n) for n = 1..13686 (terms up to 10^13)

J. O. M. Pedersen, Type system of amicable pairs

J. O. M. Pedersen, Known Amicable Pairs

Wikipedia, Regular pairs

Example

The first amicable pair (220, 284) is regular because gcd(220, 284) = 4 with 220 = 4 * (5*11) and 284 = 4 * (71). So 220 belongs to the sequence.
The second amicable pair (1184, 1210) is not regular because gcd(1184, 1210)=2 and 1184 = 2 * (2^4*37). So 1184 does not belong to the sequence.

Crossrefs

Cf. A002025, A048250.

Sequence in context: A251322 A257353 A211820 * A258537 A027797 A055663

Adjacent sequences: A215488 A215489 A215490 * A215492 A215493 A215494

Keyword

nonn

Author

Michel Marcus, Aug 13 2012

Status

approved