cp's OEIS Frontend

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

%I A373458 #15 Mar 30 2025 09:56:13
%S A373458 0,1,1,2,1,7,1,8,9,21,1,59,1,71,106,128,1,499,1,637,778,1035,1,4235,
%T A373458 625,4109,6561,8535,1,39192,1,32768,59170,65553,18026,308219,1,262163,
%U A373458 531610,602413,1,2659706,1,2098483,5173594,4194327,1,22737515,117649,18730341
%N A373458 Expansion of Sum_{p prime} x^p/(1 - p*x^p).
%F A373458 a(n) = Sum_{p|n prime} p^(n/p - 1).
%F A373458 If p is prime, a(p) = 1.
%p A373458 A373458 := proc(n)
%p A373458     local a,d ;
%p A373458     a := 0 ;
%p A373458     for d in numtheory[divisors](n) do
%p A373458         if isprime(d) then
%p A373458             a := a+d^(n/d-1) ;
%p A373458         end if;
%p A373458     end do:
%p A373458     a ;
%p A373458 end proc:
%p A373458 seq(A373458(n),n=1..20) ; # _R. J. Mathar_, Jun 07 2024
%t A373458 a[n_]:=Sum[Boole[PrimeQ[d]]d^(n/d-1),{d,Divisors[n]}]; Array[a,50] (* _Stefano Spezia_, Mar 30 2025 *)
%o A373458 (PARI) a(n) = sumdiv(n, d, isprime(d)*d^(n/d-1));
%Y A373458 Cf. A001221, A305614, A373459.
%K A373458 nonn,easy
%O A373458 1,4
%A A373458 _Seiichi Manyama_, Jun 06 2024