A333748 Number of nonprime divisors of n that are <= sqrt(n).

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

Offset: 1

Author

Ilya Gutkovskiy, Apr 03 2020

Keywords

• nonn

Crossrefs

Cf. A018252, A033273, A038548, A063962, A069288, A069291, A333749, A333750, A333751.

Programs

Mathematica

Table[DivisorSum[n, 1 &, # <= Sqrt[n] && !PrimeQ[#] &], {n, 1, 100}]
nmax = 100; CoefficientList[Series[Sum[Boole[!PrimeQ[k]] x^(k^2)/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

PARI

a(n) = sumdiv(n, d, (d^2<=n) && !isprime(d)); \\ Michel Marcus, Apr 03 2020

Formula

G.f.: Sum_{k>=1} x^(A018252(k)^2) / (1 - x^A018252(k)).