A346770 Expansion of g.f. Product_{k>=1} (1 - x^k)^phi(k), where phi() is the Euler totient function (A000010).

1, -1, -1, -1, 0, 0, 3, 1, 4, 2, 3, -5, 1, -13, -5, -13, -6, -22, 12, -12, 35, 17, 59, 11, 101, -1, 81, -35, 45, -165, 29, -311, -69, -383, -57, -501, 181, -501, 425, -191, 990, -70, 1844, 64, 2305, 183, 2625, -951, 2897, -2701, 1845, -4851, 664, -8824, 670, -12366, 269, -14137, 2884

Offset

0,7

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Formula

G.f.: exp(-Sum_{k>=1} A057660(k) * x^k/k).

a(0) = 1, a(n) = -(1/n) * Sum_{k=1..n} A057660(k) * a(n-k) for n > 0.

Prog

(PARI) N=66; x='x+O('x^N); Vec(prod(k=1, N, (1-x^k)^eulerphi(k)))
(PARI) N=66; x='x+O('x^N); Vec(exp(-sum(k=1, N, sigma(k^2, 2)/sigma(k^2)*x^k/k)))

Crossrefs

Convolution inverse of A061255.

Cf. A000010, A057660, A293116, A299069.

Sequence in context: A209919 A116537 A194307 * A048225 A155481 A075148

Adjacent sequences: A346767 A346768 A346769 * A346771 A346772 A346773

Keyword

sign

Author

Seiichi Manyama, Aug 02 2021

Status

approved