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%I #26 Oct 17 2019 01:57:40
%S 1184,1210,2620,2924,5020,5564,10744,10856,66928,66992,67095,71145,
%T 122368,123152,171856,176336,176272,180848,196724,202444,437456,
%U 455344,503056,514736,522405,525915,1077890,1099390,1154450,1189150,1280565,1340235,1358595,1486845,1392368,1464592,2082464,2090656
%N Amicable pairs with the property that both members have the same number of divisors.
%C Amicable pairs(x,y) such that d(x) = d(y), where d(n) is the number of divisors of n.
%H Amiram Eldar, <a href="/A328064/b328064.txt">Table of n, a(n) for n = 1..20000</a>
%e Consider the amicable pair [1184, 1210]. The smaller member has 12 divisors, they are 1, 2, 4, 8, 16, 32, 37, 74, 148, 296, 592, 1184. The larger member has 12 divisors, they are 1, 2, 5, 10, 11, 22, 55, 110, 121, 242, 605, 1210. The number of divisors of 1184 is equal to the number of divisors of 1210, so the amicable pair [1184, 1210] is in the sequence.
%t seq = {}; s[n_] := DivisorSigma[1, n] - n; Do[m = s[n]; If[m > n && s[m] == n && DivisorSigma[0, n] == DivisorSigma[0, m], seq = Join[seq, {n, m}]], {n, 1, 10^6}]; seq (* _Amiram Eldar_, Oct 11 2019 *)
%Y Subsequence of A259180.
%Y Cf. A000005, A002025, A002046, A328009, A328043, A328063, A328065, A328255.
%K nonn
%O 1,1
%A _Omar E. Pol_, Oct 03 2019
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