A328064 Amicable pairs with the property that both members have the same number of divisors.

1184, 1210, 2620, 2924, 5020, 5564, 10744, 10856, 66928, 66992, 67095, 71145, 122368, 123152, 171856, 176336, 176272, 180848, 196724, 202444, 437456, 455344, 503056, 514736, 522405, 525915, 1077890, 1099390, 1154450, 1189150, 1280565, 1340235, 1358595, 1486845, 1392368, 1464592, 2082464, 2090656

Offset: 1

Author

Omar E. Pol, Oct 03 2019

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

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

Crossrefs

Subsequence of A259180.

Cf. A000005, A002025, A002046, A328009, A328043, A328063, A328065, A328255.

Programs

Mathematica

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 *)