A050392 Exponential reversion of Euler totient function A000010.

1, -1, 1, 3, -39, 257, -909, -6389, 183715, -2326009, 15050003, 140089725, -6804608381, 130909360315, -1286161585477, -12952744700713, 970148927462835, -25588194678272039, 347909302401071797

Offset

1,4

Links

Table of n, a(n) for n=1..19.

N. J. A. Sloane, Transforms

Index entries for reversions of series

Formula

E.g.f. A(x) satisfies: A(x) = x - Sum_{k>=2} phi(k) * A(x)^k / k!. - Ilya Gutkovskiy, Apr 22 2020

Mathematica

length = 20; Range[length]! InverseSeries[Sum[EulerPhi[n] x^n/n!, {n, 1, length}] + O[x]^(length+1)][[3]] (* Vladimir Reshetnikov, Nov 07 2015 *)

Prog

(PARI) seq(n)= Vec(serlaplace(serreverse(sum(k=1, n, eulerphi(k)*x^k/k!) + O(x*x^n)))); \\ Michel Marcus, Apr 21 2020

Crossrefs

Cf. A000010, A050391.

Sequence in context: A292542 A212664 A342969 * A292294 A366995 A191468

Adjacent sequences: A050389 A050390 A050391 * A050393 A050394 A050395

Keyword

sign

Author

Christian G. Bower, Nov 15 1999

Status

approved