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

Author

Michel Marcus, Aug 13 2012

Keywords

• nonn

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

Examples

			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.
		

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

Crossrefs

Cf. A002025, A048250.