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A215491 Smaller members of regular amicable pairs.

%I A215491 #38 Feb 24 2022 23:34:59
%S A215491 220,2620,5020,10744,17296,63020,66928,67095,69615,100485,122265,
%T A215491 142310,171856,176272,185368,196724,308620,356408,437456,503056,
%U A215491 522405,600392,609928,624184,635624,643336,667964,726104,898216,947835,998104,1077890,1154450
%N A215491 Smaller members of regular amicable pairs.
%C A215491 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.
%C A215491 A regular amicable pair (M, K) has the property A048250(M) = A048250(K). - _Jonathan Pappas_, Jan 30 2022
%C A215491 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
%H A215491 Michel Marcus and Jonathan Pappas, <a href="/A215491/b215491.txt">Table of n, a(n) for n = 1..13686</a> (terms up to 10^13)
%H A215491 J. O. M. Pedersen, <a href="http://amicable.homepage.dk/apstat.htm#typesys">Type system of amicable pairs</a>
%H A215491 J. O. M. Pedersen, <a href="http://amicable.homepage.dk/knwnc2.htm">Known Amicable Pairs</a>
%H A215491 Wikipedia, <a href="http://en.wikipedia.org/wiki/Amicable_numbers#Regular_pairs">Regular pairs</a>
%e A215491 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.
%e A215491 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.
%Y A215491 Cf. A002025, A048250.
%K A215491 nonn
%O A215491 1,1
%A A215491 _Michel Marcus_, Aug 13 2012