A141264 Number of divisors of m^2 where m is the smallest number with exactly n divisors.

1, 3, 5, 9, 9, 15, 13, 21, 25, 27, 21, 45, 25, 39, 45, 63, 33, 75, 37, 81, 65, 63, 45, 105, 81, 75, 125, 117, 57, 135, 61, 189, 105, 99, 117, 225, 73, 111, 125, 243, 81, 195, 85, 189, 225, 135, 93, 315, 169, 243, 165, 225, 105, 375, 189, 351, 185, 171, 117, 405, 121, 183

Offset: 1

Author

J. Lowell, Aug 30 2008

Keywords

• nonn

Comments

Variant of A103578.

Examples

			a(8) = 21 because the smallest number with 8 divisors is 24, 24^2 = 576 and 576 has 21 divisors.
		

Links

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

Crossrefs

Cf. A000005, A005179, A103578.

Programs

Mathematica

a[n_]:=Module[{m=0},Until[DivisorSigma[0,m]==n,m++];DivisorSigma[0,m^2]];Array[a,25] (* James C. McMahon, Jul 26 2025 *)

Formula

a(n) = A000005(A005179(n)^2). - R. J. Mathar, Aug 31 2008

Extensions

Extended beyond a(8) by R. J. Mathar, Sep 01 2008