A333957 E.g.f. A(x) satisfies: A(x) = x - Sum_{k>=2} sigma(k) * A(x)^k / k!.

1, -3, 23, -292, 5194, -118879, 3327092, -110077602, 4202995203, -181898058107, 8799087726483, -470477273391491, 27552899058423712, -1753972172620598718, 120590533350099961096, -8905268067453051058302, 702994242229769687066025, -59076500305914641133294712

Offset

1,2

Comments

Exponential reversion of the sum of divisors function (A000203).

Links

Table of n, a(n) for n=1..18.

Index entries for reversions of series

Mathematica

nmax = 18; CoefficientList[InverseSeries[Series[Sum[DivisorSigma[1, k] x^k/k!, {k, 1, nmax}], {x, 0, nmax}], x], x] Range[0, nmax]! // Rest

Prog

(PARI) seq(n)= Vec(serlaplace(serreverse(sum(k=1, n, sigma(k)*x^k/k!) + O(x*x^n)))) \\ Michel Marcus, Apr 22 2020

Crossrefs

Cf. A000203, A050390, A333956.

Sequence in context: A363137 A060090 A052842 * A343849 A307418 A365546

Adjacent sequences: A333954 A333955 A333956 * A333958 A333959 A333960

Keyword

sign

Author

Ilya Gutkovskiy, Apr 22 2020

Status

approved