

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).


0



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
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OFFSET

2,2


COMMENTS

Its irrationality was conjectured by Erdős and Kac in 1953 and was proved by SchlagePuchta 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.
JanChristoph SchlagePuchta, The irrationality of a number theoretical series, The Ramanujan Journal, Vol. 12, No. 3 (2006), pp. 455460, 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: A175013 A210616 A238167 * A076418 A059910 A019837
Adjacent sequences: A307033 A307034 A307035 * A307037 A307038 A307039


KEYWORD

nonn,cons


AUTHOR

Amiram Eldar, Mar 21 2019


STATUS

approved



