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

1,1

Comments

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

Links

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

Example

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.

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 *)

Crossrefs

Subsequence of A259180 and of A328063.

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

Sequence in context: A287026 A233538 A328063 * A287011 A333929 A157107

Adjacent sequences: A328062 A328063 A328064 * A328066 A328067 A328068

Keyword

nonn

Author

Omar E. Pol, Oct 03 2019

Status

approved