A103578 Number of divisors of m^2, where m is the smallest number with at least n divisors.

1, 3, 5, 9, 15, 15, 21, 21, 25, 27, 45, 45, 63, 63, 63, 63, 75, 75, 81, 81, 105, 105, 105, 105, 135, 135, 135, 135, 135, 135, 189, 189, 225, 225, 225, 225, 243, 243, 243, 243, 315, 315, 315, 315, 315, 315, 315, 315, 405, 405, 405, 405, 405, 405, 405, 405, 405

Offset: 1

Author

Stefan Steinerberger, Aug 31 2008

Keywords

• nonn

Examples

			a(8) = 21 because 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, A061799, A141264.

Programs

Mathematica

a = {}; i = 1; For[n = 1, n < 60, n++, While[DivisorSigma[0, i] < n, i++ ]; AppendTo[a, DivisorSigma[0, i^2]]]; a (* Stefan Steinerberger, Aug 31 2008 *)

Formula

a(n) = A000005((A061799(n))^2). - R. J. Mathar, Sep 01 2008

Extensions

Edited by R. J. Mathar, Sep 01 2008, Dec 15 2008

Extended beyond a(8) by R. J. Mathar, Aug 31 2008