A328065 - OEIS

%I #35 Oct 16 2019 21:10:31

%S 220,284,12285,14595,17296,18416,63020,76084,69615,87633,79750,88730,

%T 100485,124155,122265,139815,142310,168730,185368,203432,308620,

%U 389924,356408,399592,600392,669688,609928,686072,624184,691256,635624,712216,643336,652664,667964,783556,726104,796696,898216,980984

%N Amicable pairs with the property that the number of divisors of the smaller member is twice the number of divisors of the larger member.

%C Amicable pairs(x,y) such that d(x) = 2*d(y), where d(n) is the number of divisors of n.

%H Amiram Eldar, <a href="/A328065/b328065.txt">Table of n, a(n) for n = 1..20000</a>

%e Consider the amicable pair [220, 284]. The smaller member has 12 divisors, they are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, 220. The larger member has 6 divisors, they are 1, 2, 4, 71, 142, 284. The number of divisors of 220 is twice the number of divisors of 284, so the amicable pair [220, 284] 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] == 2 * DivisorSigma[0, m], seq = Join[seq, {n, m}]], {n, 1, 10^6}]; seq (* _Amiram Eldar_, Oct 11 2019 *)

%Y Subsequence of A259180 and of A328063.

%Y Cf. A000005, A002025, A002046, A062011, A328009, A328043, A328064, A328255.

%K nonn

%O 1,1

%A _Omar E. Pol_, Oct 03 2019