A307781 - OEIS

%I #12 May 01 2019 05:42:45

%S 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,

%T 15,-19,26,-28,27,-30,29,-34,41,-66,66,-100,99,-163,170,-223,222,-323,

%U 322,-420,453,-622,621,-771,770,-997,1121,-1363,1362,-1851,1883,-2562,3073,-3857,3856

%N a(1) = 1; a(n+1) = -Sum_{d|n} a(d)^(n/d).

%H Robert Israel, <a href="/A307781/b307781.txt">Table of n, a(n) for n = 1..10000</a>

%F L.g.f.: log(Product_{n>=1} (1 - a(n)*x^n)^(1/n)) = Sum_{n>=1} a(n+1)*x^n/n.

%p f:= proc(n) option remember; local d;

%p   -add(procname(d)^((n-1)/d), d = numtheory:-divisors(n-1))

%p end proc:

%p f(1):= 1:

%p map(f, [$1..100]); # _Robert Israel_, Apr 29 2019

%t a[n_] := a[n] = -Sum[a[d]^((n - 1)/d), {d, Divisors[n - 1]}]; a[1] = 1; Table[a[n], {n, 1, 60}]

%o (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

%Y Cf. A127525, A307780.

%K sign

%O 1,9

%A _Ilya Gutkovskiy_, Apr 28 2019