A328065 Amicable pairs with the property that the number of divisors of the smaller member is twice the number of divisors of the larger member.

220, 284, 12285, 14595, 17296, 18416, 63020, 76084, 69615, 87633, 79750, 88730, 100485, 124155, 122265, 139815, 142310, 168730, 185368, 203432, 308620, 389924, 356408, 399592, 600392, 669688, 609928, 686072, 624184, 691256, 635624, 712216, 643336, 652664, 667964, 783556, 726104, 796696, 898216, 980984

Offset: 1

Author

Omar E. Pol, Oct 03 2019

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..20000

Crossrefs

Subsequence of A259180 and of A328063.

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

Programs

Mathematica

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 *)