A373458 Expansion of Sum_{p prime} x^p/(1 - p*x^p).

0, 1, 1, 2, 1, 7, 1, 8, 9, 21, 1, 59, 1, 71, 106, 128, 1, 499, 1, 637, 778, 1035, 1, 4235, 625, 4109, 6561, 8535, 1, 39192, 1, 32768, 59170, 65553, 18026, 308219, 1, 262163, 531610, 602413, 1, 2659706, 1, 2098483, 5173594, 4194327, 1, 22737515, 117649, 18730341

Offset: 1

Author

Seiichi Manyama, Jun 06 2024

Keywords

• nonn
• easy

Crossrefs

Cf. A001221, A305614, A373459.

Programs

Maple

A373458 := proc(n)
    local a,d ;
    a := 0 ;
    for d in numtheory[divisors](n) do
        if isprime(d) then
            a := a+d^(n/d-1) ;
        end if;
    end do:
    a ;
end proc:
seq(A373458(n),n=1..20) ; # R. J. Mathar, Jun 07 2024

Mathematica

a[n_]:=Sum[Boole[PrimeQ[d]]d^(n/d-1),{d,Divisors[n]}]; Array[a,50] (* Stefano Spezia, Mar 30 2025 *)

PARI

a(n) = sumdiv(n, d, isprime(d)*d^(n/d-1));

Formula

a(n) = Sum_{p|n prime} p^(n/p - 1).

If p is prime, a(p) = 1.