A367325 Decimal expansion of Sum_{k>=1} sigma(k)/(2^k-1), where sigma(k) is the sum of divisors of k (A000203).

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

Offset

1,1

Links

Table of n, a(n) for n=1..105.

Maxie Dion Schmidt, A catalog of interesting and useful Lambert series identities, arXiv:2004.02976 [math.NT], 2020. See eq. (6.1c), p. 13.

Michael I. Shamos, Shamos's catalog of the real numbers, 2011. See p. 526.

Formula

Equals Sum_{k>=1} d(k)/((2^k-1)*(1-1/2^k)), where d(k) is the number of divisors of k (A000005).

Example

3.60444734197194674489364847362358835600495487064998...

Maple

with(numtheory): evalf(sum(sigma(k)/(2^k-1), k = 1..infinity), 120)

Mathematica

RealDigits[Sum[DivisorSigma[1, n]/(2^n-1), {n, 1, 500}], 10, 120][[1]]

Prog

(PARI) suminf(k = 1, sigma(k)/(2^k-1))
(PARI) suminf(k = 1, numdiv(k)/((2^k-1)*(1-1/2^k)))

Crossrefs

Cf. A000005, A000203.

Similar constants: A065442, A066766, A116217, A335763, A335764.

Sequence in context: A182196 A334477 A278488 * A038023 A008954 A169890

Adjacent sequences: A367322 A367323 A367324 * A367326 A367327 A367328

Keyword

nonn,cons

Author

Amiram Eldar, Nov 14 2023

Status

approved