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%I #18 Apr 04 2023 12:35:03
%S 1,-4,-9,0,-25,36,-49,0,0,100,-121,0,-169,196,225,0,-289,0,-361,0,441,
%T 484,-529,0,0,676,0,0,-841,-900,-961,0,1089,1156,1225,0,-1369,1444,
%U 1521,0,-1681,-1764,-1849,0,0,2116,-2209,0,0,0,2601,0,-2809,0,3025,0,3249,3364,-3481,0,-3721
%N Dirichlet g.f.: 1 / zeta(s-2).
%C Dirichlet inverse of A000290.
%C Moebius transform of A046970.
%C Inverse Moebius transform of A053822.
%H Amiram Eldar, <a href="/A334657/b334657.txt">Table of n, a(n) for n = 1..10000</a>
%F G.f. A(x) satisfies: A(x) = x - 2^2 * A(x^2) - 3^2 * A(x^3) - 4^2 * A(x^4) - ...
%F a(1) = 1; a(n) = -n^2 * Sum_{d|n, d < n} a(d) / d^2.
%F a(n) = mu(n) * n^2.
%F Multiplicative with a(p^e) = -p^2 if e = 1 and 0 otherwise. - _Amiram Eldar_, Oct 25 2020
%t Table[MoebiusMu[n] n^2, {n, 61}]
%Y Cf. A008683, A055615, A334659, A334660.
%Y Cf. A000290, A046970, A053822.
%K sign,mult,easy
%O 1,2
%A _Ilya Gutkovskiy_, May 07 2020