A093616 a(n) is the smallest k such that k*n has exactly as many divisors as n^2.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 8, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 8, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72

Offset: 1

Author

Reinhard Zumkeller, Apr 06 2004

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A000290, A048691, A093617, A093618.

Programs

Mathematica

a[n_] := For[k = 1, True, k++, If[DivisorSigma[0, k*n] == DivisorSigma[0, n^2], Return[k]]]; Array[a, 72] (* Jean-François Alcover, Aug 14 2014 *)

PARI

a(n) = {my(k = 1, d = numdiv(n^2)); while(numdiv(k*n) != d, k++); k;} \\ Amiram Eldar, Apr 15 2024

Formula

A000005(a(n)*n) = A000005(n^2) and A000005(m*n) <> A000005(n^2) for m < a(n).

a(A093617(n)) < n, a(A093618(n)) = n.