A325257 a(1) = 1; a(n) = Sum_{d|n, d

1, 3, 5, 16, 11, 43, 17, 88, 48, 95, 31, 320, 41, 145, 157, 486, 59, 554, 67, 696, 243, 265, 83, 2204, 218, 347, 458, 1062, 109, 1961, 127, 2668, 447, 493, 523, 5044, 157, 565, 577, 4780, 179, 3021, 191, 1938, 1998, 697, 211, 14590, 516, 2538, 823, 2526, 241, 6622, 939

Offset: 1

Author

Ilya Gutkovskiy, Sep 05 2019

Keywords

• nonn

Crossrefs

Cf. A000040, A007445, A008966 (parity of a(n)), A034696.

Programs

Magma

sol:=[1]; for n in [2..60] do Append(~sol,&+[NthPrime(Floor(n/d))*sol[d]:d in Set(Divisors(n)) diff {n}]); end for; sol; // Marius A. Burtea, Sep 05 2019

Mathematica

a[n_] := If[n == 1, n, Sum[If[d < n, Prime[n/d] a[d], 0], {d, Divisors[n]}]]; Table[a[n], {n, 1, 55}]
nmax = 55; A[] = 0; Do[A[x] = x + Sum[Prime[k] A[x^k], {k, 2, nmax}] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] // Rest

PARI

seq(n)={my(v=vector(n)); v[1]=1; for(n=2, #v, v[n] = sumdiv(n, d, v[d]*prime(n/d))); v} \\ Andrew Howroyd, Sep 05 2019

Formula

G.f. A(x) satisfies: A(x) = x + Sum_{k>=2} prime(k) * A(x^k).