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A359060
Decimal expansion of Sum_{n >= 1} sigma_4(n)/n!.
1
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
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
KEYWORD
cons,nonn
AUTHOR
STATUS
approved