A321516 Number of composite divisors of n that are < n.

0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 4, 0, 0, 1, 2, 0, 3, 0, 3, 0, 0, 0, 5, 0, 0, 0, 4, 0, 3, 0, 2, 2, 0, 0, 6, 0, 2, 0, 2, 0, 4, 0, 4, 0, 0, 0, 7, 0, 0, 2, 4, 0, 3, 0, 2, 0, 3, 0, 8, 0, 0, 2, 2, 0, 3, 0, 6, 2, 0, 0, 7, 0, 0, 0

Offset: 1

Author

Felix Fröhlich, Nov 12 2018

Keywords

• nonn

Comments

Different from A294902 (see A321517).

a(n) > 0 iff n is a term of A033942.

Examples

			For n = 24: The divisors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. Four of those divisors, namely 4, 6, 8 and 12 are composite and < 24, so a(24) = 4.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A033942, A294902, A321517.

Programs

Mathematica

a[n_] := Length[Select[Most[Divisors[n]], CompositeQ]]; Array[a, 87] (* Amiram Eldar, Nov 12 2018 *)

PARI

a(n) = my(d=divisors(n), i=0); for(k=2, #d-1, if(!ispseudoprime(d[k]), i++)); i

PARI

a(n) = sumdiv(n, d, (d1) && !isprime(d)); \\ Michel Marcus, Nov 12 2018