A193335 Number of odd divisors of sigma(n).

1, 2, 1, 2, 2, 2, 1, 4, 2, 3, 2, 2, 2, 2, 2, 2, 3, 4, 2, 4, 1, 3, 2, 4, 2, 4, 2, 2, 4, 3, 1, 6, 2, 4, 2, 4, 2, 4, 2, 6, 4, 2, 2, 4, 4, 3, 2, 2, 4, 4, 3, 3, 4, 4, 3, 4, 2, 6, 4, 4, 2, 2, 2, 2, 4, 3, 2, 6, 2, 3, 3, 8, 2, 4, 2, 4, 2, 4, 2, 4

Offset: 1

Author

Michel Lagneau, Jul 23 2011

Keywords

• nonn

Examples

			a(8) = 4 because sigma(8) = 15 and the 4 odd divisors are { 1, 3, 5, 15}.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000203 (sigma), A001227.

Programs

Mathematica

f[n_] := Block[{d = Divisors[DivisorSigma[1,n]]}, Count[OddQ[d], True]]; Table[f[n], {n, 80}]
Table[Count[Divisors[DivisorSigma[1,n]],?OddQ],{n,80}] (* _Harvey P. Dale, Jul 06 2019 *)
odd[n_] := DivisorSigma[0, n / 2^IntegerExponent[n, 2]]; a[n_] := odd[DivisorSigma[1, n]]; Array[a, 100] (* Amiram Eldar, Jul 06 2022 *)

PARI

a(n)=sumdiv(sigma(n,1),d,d%2);

PARI

a(n)=n=sigma(n);numdiv(n>>valuation(n,2)) \\ Charles R Greathouse IV, Jul 30 2011

Formula

a(n) = A001227(A000203(n)). - Michel Marcus, Jan 14 2014