OFFSET
1,2
LINKS
Ramanujan's Papers, Some formulas in the analytic theory of numbers, Messenger of Mathematics, XLV, 1916, 81-84, Formula (20), constant c.
FORMULA
Equals exp(1) * lim_{n->infinity} (A066780(n)^(1/n)) / n.
EXAMPLE
1.561596846931024164326967889144555644364737646822232169945866457...
MATHEMATICA
$MaxExtraPrecision = 1000; m = 500; prod = 1; Do[Clear[f]; f[p_] := ((p^(k + 1) - 1)/(p^(k + 1) - p))^(1/p^k); cc = Rest[CoefficientList[Series[Log[f[1/x]], {x, 0, m}], x, m + 1]]; prod *= f[2]*Exp[N[Sum[Indexed[cc, n]*(PrimeZetaP[n] - 1/2^n), {n, 2, m}], 100]]; Print[prod], {k, 1, 200}]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Vaclav Kotesovec, Jun 09 2021
STATUS
approved