A333751 Sum of nonprime divisors of n that are <= sqrt(n).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 5, 1, 1, 1, 5, 1, 1, 1, 5, 1, 1, 1, 5, 1, 1, 1, 11, 1, 1, 1, 5, 1, 7, 1, 5, 1, 1, 1, 11, 1, 1, 1, 5, 1, 7, 1, 5, 1, 1, 1, 11, 1, 1, 1, 13, 1, 7, 1, 5, 1, 1, 1, 19, 1, 1, 1, 5, 1, 7, 1, 13, 10, 1, 1, 11, 1, 1, 1, 13, 1, 16

Offset: 1

Author

Ilya Gutkovskiy, Apr 03 2020

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A018252, A023890, A066839, A069289, A069293, A097974, A333748, A333752, A333753.

Programs

Maple

f:= proc(n) convert(select(t -> not isprime(t) and t^2 <= n, numtheory:-divisors(n)),`+`) end proc:
map(f, [$1..100]); # Robert Israel, Sep 12 2024

Mathematica

Table[DivisorSum[n, # &, # <= Sqrt[n] && !PrimeQ[#] &], {n, 1, 90}]
nmax = 90; CoefficientList[Series[Sum[Boole[!PrimeQ[k]] k x^(k^2)/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

PARI

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

Formula

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