A359531 a(1) = 1, a(2) = -9; a(n) = -n^3 * Sum_{d|n, d < n} a(d) / d^3.

1, -9, -27, 8, -125, 243, -343, 0, 0, 1125, -1331, -216, -2197, 3087, 3375, 0, -4913, 0, -6859, -1000, 9261, 11979, -12167, 0, 0, 19773, 0, -2744, -24389, -30375, -29791, 0, 35937, 44217, 42875, 0, -50653, 61731, 59319, 0, -68921, -83349, -79507, -10648, 0

Offset: 1

Author

Seiichi Manyama, Apr 01 2023

Keywords

• sign
• mult

Links

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

Crossrefs

Partial sums give A360658.

Cf. A092673, A359484, A359485.

Cf. A334659.

Programs

Mathematica

f[p_, e_] := If[e == 1, -p^3, 0]; f[2, e_] := Switch[e, 1, -9, 2, 8, , 0]; a[1] = 1; a[n] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, May 10 2023 *)

Formula

a(n) is multiplicative with a(2)= -9, a(4)= 8, a(2^e)= 0 if e>2. a(p)= -p^3, a(p^e)= 0 if e>1, p>2.

G.f. A(x) satisfies x * (1 - x) = Sum_{k>=1} k^3 * A(x^k).