A361986 a(1) = 1, a(2) = 3; a(n) = n^2 * Sum_{d|n, d < n} (-1)^(n/d) a(d) / d^2.

1, 3, -9, 28, -25, -27, -49, 224, 0, -75, -121, -252, -169, -147, 225, 1792, -289, 0, -361, -700, 441, -363, -529, -2016, 0, -507, 0, -1372, -841, 675, -961, 14336, 1089, -867, 1225, 0, -1369, -1083, 1521, -5600, -1681, 1323, -1849, -3388, 0, -1587, -2209, -16128, 0, 0, 2601, -4732, -2809, 0, 3025, -10976

Offset: 1

Author

Seiichi Manyama, Apr 02 2023

Keywords

• sign
• mult

Links

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

Crossrefs

Partial sums give A361981.

Cf. A361984, A361985.

Cf. A359485.

Programs

Mathematica

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 *)

Formula

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.

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