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%I #20 Aug 27 2023 04:22:56
%S 1,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%T 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,
%U 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N Dirichlet inverse of A154281.
%C Sequence is positive as often as negative.
%C Multiplicative because A154281 is. - _Andrew Howroyd_, Aug 05 2018
%H Mats Granvik, <a href="/A154282/b154282.txt">Table of n, a(n) for n = 1..1500</a>
%F Multiplicative with a(2^e) = (-1)^(e/2) if e is even and 0 is e is odd, and a(p^e) = 0 if p is an odd prime. - _Amiram Eldar_, Aug 27 2023
%t nn = 95; a = PadRight[{1, 0, 0, 1}, nn, 0]; Inverse[Table[Table[If[Mod[n, k] == 0, a[[n/k]], 0], {k, 1, nn}], {n, 1, nn}]][[All, 1]] (* _Mats Granvik_, Jul 23 2017 *)
%o (PARI) a(n) = {my(e=valuation(n,2)); if(e%2 == 0 && n == 1<<e, (-1)^(e/2), 0)} \\ _Andrew Howroyd_, Aug 05 2018
%Y Cf. A154269, A154271, A154272, A154281.
%K sign,easy,mult
%O 1,1
%A _Mats Granvik_, Jan 06 2009