A033272 Number of odd nonprimes dividing n.

1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 3, 1, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 1, 4, 1, 1, 1, 2, 2, 2, 1, 1, 3, 2, 1, 2, 1, 1, 2, 1, 1, 4, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 4, 1, 2, 2, 1, 1

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001227 (with odd divisors), A005087, A033273 (with nonprime divisors).

Programs

Mathematica

Table[Length[Select[Divisors[n],OddQ[#]&&!PrimeQ[#]&]],{n,80}] (* Harvey P. Dale, May 06 2012 *)
a[n_] := DivisorSigma[0, n/2^IntegerExponent[n, 2]] - PrimeNu[n] + If[OddQ[n], 0, 1]; Array[a, 100] (* Amiram Eldar, Jul 01 2022 *)

PARI

a(n) = sumdiv(n, d, (d%2) && !isprime(d)); \\ Michel Marcus, May 05 2017

Formula

a(n) = A001227(n) - A005087(n). - Amiram Eldar, Jul 01 2022