A146288 Number of divisors of the n-th prime signature number (A025487(n)).

1, 2, 3, 4, 4, 6, 5, 8, 8, 6, 9, 10, 12, 7, 12, 12, 16, 8, 15, 18, 14, 16, 16, 20, 9, 18, 24, 16, 24, 20, 24, 10, 21, 30, 18, 32, 24, 27, 28, 11, 32, 24, 36, 25, 36, 20, 40, 28, 36, 32, 12, 40, 27, 32, 48, 30, 42, 22, 48, 32, 45, 36, 13, 48, 30, 48, 60, 35, 48, 48, 24, 54, 50, 56

Offset: 1

Author

Matthew Vandermast, Nov 11 2008

Keywords

• nonn

Examples

			a(4) = 4 because 4 positive integers divide evenly into A025487(4) = 6: 1, 2, 3 and 6.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

a(n) = sum of the n-th row of A146290, A146292.

A rearrangement of A080444.

Cf. A000005 (number of divisors), A025487.

Programs

Haskell

a146288 = a000005 . a025487  -- Reinhard Zumkeller, Sep 17 2014

Mathematica

s = {1}; Do[If[GreaterEqual @@ (f = FactorInteger[n])[[;; , 2]] && PrimePi[f[[-1, 1]]] == Length[f], AppendTo[s, DivisorSigma[0, n]]], {n, 2, 10000}]; s (* Amiram Eldar, Aug 05 2024 *)

Formula

a(n) = A000005(A025487(n)).