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

1,1

Comments

Amicable pairs(x,y) such that d(x) = 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 [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.

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 *)

Crossrefs

Subsequence of A259180.

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

Sequence in context: A210847 A320716 A269017 * A280516 A205994 A345540

Adjacent sequences: A328061 A328062 A328063 * A328065 A328066 A328067

Keyword

nonn

Author

Omar E. Pol, Oct 03 2019

Status

approved