A335062 - OEIS

%I #10 Dec 09 2021 17:24:21

%S 1,0,2,0,2,-2,2,0,4,-2,2,0,2,-2,6,0,2,-8,2,0,6,-2,2,0,4,-2,8,0,2,-14,

%T 2,0,6,-2,6,4,2,-2,6,0,2,-14,2,0,16,-2,2,0,4,-8,6,0,2,-24,6,0,6,-2,2,

%U 8,2,-2,16,0,6,-14,2,0,6,-14,2,0,2,-2,16,0,6,-14,2,0,16

%N a(n) = 1 - Sum_{d|n, d > 1} (-1)^d * a(n/d).

%C Inverse Moebius transform of A308077.

%H Antti Karttunen, <a href="/A335062/b335062.txt">Table of n, a(n) for n = 1..20000</a>

%F G.f. A(x) satisfies: A(x) = x / (1 - x) - Sum_{k>=2} (-1)^k * A(x^k).

%t a[n_] := a[n] = 1 - DivisorSum[n, (-1)^# a[n/#] &, # > 1 &]; Table[a[n], {n, 1, 81}]

%o (PARI) lista(nn) = {my(va = vector(nn)); for (n=1, nn, va[n] = 1 - sumdiv(n, d, if (d>1, (-1)^d*va[n/d]));); va;} \\ _Michel Marcus_, May 22 2020

%Y Cf. A048298, A065091 (positions of 2's), A067824, A067856, A308077, A325144, A335283.

%K sign

%O 1,3

%A _Ilya Gutkovskiy_, May 21 2020