A325891
a(1) = 1; a(n) = -Sum_{d|n, 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
Keywords
Programs
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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 -
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
a(n) = if (n==1, 1, -sumdiv(n, d, if (d
Formula
G.f. A(x) satisfies: A(x) = x - Sum_{k>=2} prime(k) * A(x^k).