A359060 Decimal expansion of Sum_{n >= 1} sigma_4(n)/n!.

4, 2, 3, 0, 1, 0, 4, 7, 5, 0, 3, 7, 3, 3, 5, 0, 8, 0, 6, 6, 8, 6, 4, 2, 8, 4, 0, 6, 2, 5, 3, 0, 7, 6, 4, 5, 3, 0, 5, 9, 5, 6, 7, 0, 6, 2, 2, 4, 9, 3, 3, 2, 3, 1, 5, 5, 1, 1, 8, 8, 7, 6, 9, 4, 9, 4, 2, 6, 8, 9, 9, 1, 3, 1, 9, 7, 6, 5, 8, 1, 2

Offset

2,1

Comments

This constant's irrationality was conjectured by Erdős and Kac in 1953 and proved by Pratt in 2022.

Links

Table of n, a(n) for n=2..82.

Paul Erdős and Mark Kac, Problem 4518, American Mathematical Monthly, Vol. 60, No. 1 (1953), p. 47.

Kyle Pratt, The irrationality of a divisor function series of Erdős and Kac, arXiv preprint, arXiv:2209.11124 [math.NT], 2022.

Example

42.301047503733508066864284062530764530595670622493323155118876949426899131....

Mathematica

RealDigits[N[Sum[DivisorSigma[4, n]/n!, {n, 1, 500}], 120]][[1]] (* Amiram Eldar, Jun 21 2023 *)

Prog

(PARI) suminf(n=1, sigma(n, 4)/n!)

Crossrefs

Sum_{n >= 1} sigma_k(n)/n!: A227988 (k=1), A227989 (k=2), A307036 (k=3), this sequence (k=4).

Sequence in context: A350609 A261253 A328334 * A134977 A199081 A338106

Adjacent sequences: A359057 A359058 A359059 * A359061 A359062 A359063

Keyword

cons,nonn

Author

Charles R Greathouse IV, Dec 14 2022

Status

approved