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

1,2

Links

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

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

Example

(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.

Mathematica

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

Prog

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

Crossrefs

Cf. A000005, A083399, A086971, A100959.

Cf. A064911, A027750.

Sequence in context: A081309 A329377 A010553 * A163374 A108502 A260235

Adjacent sequences: A262092 A262093 A262094 * A262096 A262097 A262098

Keyword

nonn,easy

Author

Juri-Stepan Gerasimov, Sep 11 2015

Status

approved