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%I #17 May 10 2023 04:31:46
%S 1,3,-9,28,-25,-27,-49,224,0,-75,-121,-252,-169,-147,225,1792,-289,0,
%T -361,-700,441,-363,-529,-2016,0,-507,0,-1372,-841,675,-961,14336,
%U 1089,-867,1225,0,-1369,-1083,1521,-5600,-1681,1323,-1849,-3388,0,-1587,-2209,-16128,0,0,2601,-4732,-2809,0,3025,-10976
%N a(1) = 1, a(2) = 3; a(n) = n^2 * Sum_{d|n, d < n} (-1)^(n/d) a(d) / d^2.
%H Seiichi Manyama, <a href="/A361986/b361986.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) is multiplicative with a(2) = 3, a(2^e) = 7*2^(3*e-4) if e>1. a(p) = -p^2, a(p^e) = 0 if e>1, p>2.
%F G.f. A(x) satisfies -x * (1 - x) = Sum_{k>=1} (-1)^k * k^2 * A(x^k).
%t f[p_, e_] := If[e == 1, -p^2, 0]; f[2, e_] := If[e == 1, 3, 7*2^(3*e-4)]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, May 09 2023 *)
%Y Partial sums give A361981.
%Y Cf. A361984, A361985.
%Y Cf. A359485.
%K sign,mult
%O 1,2
%A _Seiichi Manyama_, Apr 02 2023
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