A128200 Numbers of divisors of semiprime powers: A000005(A085155(n)).

1, 3, 4, 3, 4, 4, 4, 5, 4, 4, 3, 4, 4, 4, 4, 9, 4, 4, 4, 3, 4, 4, 4, 4, 4, 7, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 4, 4, 9, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 9, 4, 4, 4, 4, 4, 4, 4, 4, 4, 16, 4, 4, 4, 4, 9, 4, 4, 4, 4, 4, 4, 4, 9, 4, 4, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4

Offset: 1

Author

Reinhard Zumkeller, Mar 04 2007

Keywords

• nonn

Comments

The range of this sequence is the union of squares and the odd numbers: A128201.

Links

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

Crossrefs

Cf. A005408, A000290.

Programs

Mathematica

sppQ[n_] := With[{f = FactorInteger[n][[All, 2]]}, n == 1 || Length[f] == 1 && EvenQ[f[[1]]] || Length[f] == 2 && f[[1]] == f[[2]]];
DivisorSigma[0, #]& /@ Select[Range[1000], sppQ] (* Jean-François Alcover, Nov 21 2020 *)

Formula

a(n) = (1+A001222(A085155(n))/A001221(A085155(n)))^A001221(A085155(n)).