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

1,2

Links

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

Formula

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A000203 (sigma), A001227.

Sequence in context: A335283 A126865 A104640 * A016727 A335420 A241318

Adjacent sequences: A193332 A193333 A193334 * A193336 A193337 A193338

Keyword

nonn

Author

Michel Lagneau, Jul 23 2011

Status

approved