A325891 a(1) = 1; a(n) = -Sum_{d|n, d<n} prime(n/d) * a(d).

1, -3, -5, 2, -11, 17, -17, -4, 2, 37, -31, -24, -41, 59, 63, 2, -59, -18, -67, -40, 97, 107, -83, 64, 24, 145, 2, -70, -109, -245, -127, 12, 173, 215, 225, 110, -157, 239, 243, 96, -179, -401, -191, -122, -46, 299, -211, -70, 62, -98, 357, -166, -241, 30, 425

Offset

1,2

Links

Table of n, a(n) for n=1..55.

Formula

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

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

Prog

(PARI) a(n) = if (n==1, 1, -sumdiv(n, d, if (d <n, prime(n/d) * a(d)))); \\ Michel Marcus, Sep 08 2019
(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

Crossrefs

Cf. A000040, A007445, A034696, A325257.

Sequence in context: A102507 A076556 A324776 * A217859 A108426 A355267

Adjacent sequences: A325888 A325889 A325890 * A325892 A325893 A325894

Keyword

sign

Author

Ilya Gutkovskiy, Sep 07 2019

Status

approved