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
Examples
14.6935328472692822331235513649820566388631939576...
Links
- 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.
Programs
-
Mathematica
RealDigits[N[Sum[DivisorSigma[3, n]/n!, {n, 1, 500}], 100]][[1]] -
PARI
suminf(k=1, sigma(k, 3)/k!) \\ Michel Marcus, Mar 21 2019
Comments