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%I #28 May 10 2023 04:31:49
%S 1,4,-9,32,-25,-36,-49,256,0,-100,-121,-288,-169,-196,225,2048,-289,0,
%T -361,-800,441,-484,-529,-2304,0,-676,0,-1568,-841,900,-961,16384,
%U 1089,-1156,1225,0,-1369,-1444,1521,-6400,-1681,1764,-1849,-3872,0,-2116,-2209,-18432,0,0,2601,-5408,-2809,0
%N a(1) = 1; a(n) = n^2 * Sum_{d|n, d < n} (-1)^(n/d) a(d) / d^2.
%H Seiichi Manyama, <a href="/A361987/b361987.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) is multiplicative with a(2^e) = 2^(3*e-1). a(p) = -p^2, a(p^e) = 0 if e>1, p>2.
%F G.f. A(x) satisfies -x = Sum_{k>=1} (-1)^k * k^2 * A(x^k).
%t f[p_, e_] := If[e == 1, -p^2, 0]; f[2, e_] := 2^(3*e - 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, May 09 2023 *)
%Y Partial sums give A361983.
%Y Cf. A067856, A332793.
%Y Cf. A334657, A361986.
%K sign,mult
%O 1,2
%A _Seiichi Manyama_, Apr 02 2023