A307036 Decimal expansion of Sum_{k >= 1} sigma_3(k)/k!, where sigma_3(k) is the sum of cubes of the divisors of k (A001158).

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

Offset

2,2

Comments

Its irrationality was conjectured by Erdős and Kac in 1953 and was proved by Schlage-Puchta in 2006 and Friedlander et al. in 2007.

Links

Table of n, a(n) for n=2..88.

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

John B. Friedlander, Florian Luca, and Mihai Stoiciu, On the irrationality of a divisor function series, Integers, Vol. 7, No. 1 (2007), A31.

Jan-Christoph Schlage-Puchta, The irrationality of a number theoretical series, The Ramanujan Journal, Vol. 12, No. 3 (2006), pp. 455-460, preprint, arXiv:1105.1452 [math.NT], 2011.

Example

14.6935328472692822331235513649820566388631939576...

Mathematica

RealDigits[N[Sum[DivisorSigma[3, n]/n!, {n, 1, 500}], 100]][[1]]

Prog

(PARI) suminf(k=1, sigma(k, 3)/k!) \\ Michel Marcus, Mar 21 2019

Crossrefs

Cf. A001158, A227988, A227989.

Sequence in context: A210616 A238167 A380876 * A076418 A059910 A385256

Adjacent sequences: A307033 A307034 A307035 * A307037 A307038 A307039

Keyword

nonn,cons

Author

Amiram Eldar, Mar 21 2019

Status

approved