A361987 a(1) = 1; a(n) = n^2 * Sum_{d|n, d < n} (-1)^(n/d) a(d) / d^2.

1, 4, -9, 32, -25, -36, -49, 256, 0, -100, -121, -288, -169, -196, 225, 2048, -289, 0, -361, -800, 441, -484, -529, -2304, 0, -676, 0, -1568, -841, 900, -961, 16384, 1089, -1156, 1225, 0, -1369, -1444, 1521, -6400, -1681, 1764, -1849, -3872, 0, -2116, -2209, -18432, 0, 0, 2601, -5408, -2809, 0

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Formula

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.

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

Mathematica

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 *)

Crossrefs

Partial sums give A361983.

Cf. A067856, A332793.

Cf. A334657, A361986.

Sequence in context: A271461 A272423 A280163 * A071378 A053192 A338576

Adjacent sequences: A361984 A361985 A361986 * A361988 A361989 A361990

Keyword

sign,mult

Author

Seiichi Manyama, Apr 02 2023

Status

approved