A262095 Number of non-semiprime divisors of n.

1, 2, 2, 2, 2, 3, 2, 3, 2, 3, 2, 4, 2, 3, 3, 4, 2, 4, 2, 4, 3, 3, 2, 6, 2, 3, 3, 4, 2, 5, 2, 5, 3, 3, 3, 6, 2, 3, 3, 6, 2, 5, 2, 4, 4, 3, 2, 8, 2, 4, 3, 4, 2, 6, 3, 6, 3, 3, 2, 8, 2, 3, 4, 6, 3, 5, 2, 4, 3, 5, 2, 9, 2, 3, 4, 4, 3, 5, 2, 8, 4, 3, 2, 8, 3, 3, 3, 6, 2, 8, 3, 4, 3, 3, 3, 10, 2

Offset: 1

Author

Juri-Stepan Gerasimov, Sep 11 2015

Keywords

• nonn
• easy

Examples

			(1, 2, 3, 4, 6, 8, 12, 24) are the divisors of n = 24: 1, 2, 3, 8, 12, and 24 are non-semiprimes, therefore a(24) = 6.
		

Links

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

Crossrefs

Cf. A000005, A083399, A086971, A100959.

Cf. A064911, A027750.

Programs

Haskell

a262095 = sum . map ((1 -) . a064911) . a027750_row
-- Reinhard Zumkeller, Sep 14 2015

Mathematica

Table[Count[Divisors@ n, x_ /; PrimeOmega@ x != 2], {n, 97}] (* Michael De Vlieger, Sep 14 2015 *)

PARI

a(n) = sumdiv(n, d, bigomega(d)!=2); \\ Michel Marcus, Sep 11 2015

PARI

a(n)=my(f=factor(n)[,2]); prod(i=1,#f,f[i]+1) - sum(i=1,#f,f[i]>1) - #f*(#f-1)/2 \\ Charles R Greathouse IV, Sep 14 2015

Formula

a(n) = A000005(n) - A086971(n).

A083399(n) <= a(n) <= A000005(n).

a(n) = Sum_{k=1..A000005(n)} (1 - A064911(A027750(n,k))). - Reinhard Zumkeller, Sep 14 2015