A307781 a(1) = 1; a(n+1) = -Sum_{d|n} a(d)^(n/d).
1, -1, 0, -1, -1, 0, 0, -1, -2, 1, -2, 1, -2, 1, -1, 1, -5, 4, -8, 7, -10, 9, -13, 12, -15, 15, -19, 26, -28, 27, -30, 29, -34, 41, -66, 66, -100, 99, -163, 170, -223, 222, -323, 322, -420, 453, -622, 621, -771, 770, -997, 1121, -1363, 1362, -1851, 1883, -2562, 3073, -3857, 3856
Offset: 1
Keywords
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
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Maple
f:= proc(n) option remember; local d; -add(procname(d)^((n-1)/d), d = numtheory:-divisors(n-1)) end proc: f(1):= 1: map(f, [$1..100]); # Robert Israel, Apr 29 2019
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Mathematica
a[n_] := a[n] = -Sum[a[d]^((n - 1)/d), {d, Divisors[n - 1]}]; a[1] = 1; Table[a[n], {n, 1, 60}] -
PARI
lista(nn) = {my(va = vector(nn)); va[1] = 1; for (n=2, nn, va[n] = -sumdiv(n-1, d, va[d]^((n-1)/d));); va;} \\ Michel Marcus, Apr 30 2019
Formula
L.g.f.: log(Product_{n>=1} (1 - a(n)*x^n)^(1/n)) = Sum_{n>=1} a(n+1)*x^n/n.