A325891 - OEIS

%I #12 Sep 08 2022 08:46:24

%S 1,-3,-5,2,-11,17,-17,-4,2,37,-31,-24,-41,59,63,2,-59,-18,-67,-40,97,

%T 107,-83,64,24,145,2,-70,-109,-245,-127,12,173,215,225,110,-157,239,

%U 243,96,-179,-401,-191,-122,-46,299,-211,-70,62,-98,357,-166,-241,30,425

%N a(1) = 1; a(n) = -Sum_{d|n, d<n} prime(n/d) * a(d).

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

%t 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}]

%t 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

%o (PARI) a(n) = if (n==1, 1, -sumdiv(n, d, if (d <n, prime(n/d) * a(d)))); \\ _Michel Marcus_, Sep 08 2019

%o (Magma) sol:=[1]; for n in [2..55] do Append(~sol,-&+[NthPrime(Floor(n/d))*sol[d]:d in Set(Divisors(n)) diff {n}]); end for; sol; // _Marius A. Burtea_, Sep 08 2019

%Y Cf. A000040, A007445, A034696, A325257.

%K sign

%O 1,2

%A _Ilya Gutkovskiy_, Sep 07 2019