OFFSET
0,1
COMMENTS
LINKS
Vladimir Shevelev, Exponentially S-numbers, arXiv:1510.05914 [math.NT], 2015-2016.
FORMULA
Equals (1/2) * Product_{p odd prime} (1 + Sum_{k>=2} (c(k)-c(k-1))/p^k), where c(k) is the characteristic function of the squares (A010052).
EXAMPLE
0.40979744671331970751092295652844049998230163939067...
MATHEMATICA
$MaxExtraPrecision = m = 1000; em = 100; f[x_] := Log[1 + Sum[x^(e^2), {e, 2, em}] - Sum[x^(e^2 + 1), {e, 1, em}]]; c = Rest[CoefficientList[Series[f[x], {x, 0, m}], x]*Range[0, m]]; RealDigits[(1/2) * Exp[NSum[Indexed[c, k]*(PrimeZetaP[k] - 1/2^k)/k, {k, 2, m}, NSumTerms -> m, WorkingPrecision -> m]], 10, 105][[1]]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, Sep 09 2022
STATUS
approved