A262095 - OEIS

%I #25 Oct 13 2018 09:14:34

%S 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,

%T 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,

%U 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

%N Number of non-semiprime divisors of n.

%H Charles R Greathouse IV, <a href="/A262095/b262095.txt">Table of n, a(n) for n = 1..10000</a>

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

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

%F a(n) = Sum_{k=1..A000005(n)} (1 - A064911(A027750(n,k))). - _Reinhard Zumkeller_, Sep 14 2015

%e (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.

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

%o (PARI) a(n) = sumdiv(n, d, bigomega(d)!=2); \\ _Michel Marcus_, Sep 11 2015

%o (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

%o (Haskell)

%o a262095 = sum . map ((1 -) . a064911) . a027750_row

%o -- _Reinhard Zumkeller_, Sep 14 2015

%Y Cf. A000005, A083399, A086971, A100959.

%Y Cf. A064911, A027750.

%K nonn,easy

%O 1,2

%A _Juri-Stepan Gerasimov_, Sep 11 2015