OFFSET
0,1
COMMENTS
Named after the Indian-American mathematician Krishnaswami Alladi (b. 1955) and the American mathematician Charles Miller Grinstead (b. 1952). - Amiram Eldar, Jun 15 2021
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, pp. 120-122.
R. K. Guy, Unsolved Problems in Number Theory, Springer, 1st edition, 1981. See section B22.
LINKS
K. Alladi and C. Grinstead, On the decomposition of n! into prime powers, J. Number Theory, Vol. 9, No. 4 (1977), pp. 452-458.
Simon Plouffe, Alladi-Grinstead Constant.
Eric Weisstein's World of Mathematics, Alladi-Grinstead Constant.
FORMULA
Equals exp(c-1), where c is Sum_{n>=1} (zeta(n+1) - 1)/n (cf. A085361).
Equals lim_{n->oo} (Product_{k=1..n} (k/n)*floor(n/k))^(1/n). - Benoit Cloitre, Jul 15 2022
EXAMPLE
0.80939402054063913071793188059409131721595399242500030424202871504...
MAPLE
evalf(exp(sum((Zeta(n+1)-1)/n, n=1..infinity)-1), 120); # Vaclav Kotesovec, Dec 11 2015
MATHEMATICA
$MaxExtraPrecision = 256; RealDigits[ Exp[ Sum[ N[(-1 + Zeta[1 + n])/n, 256], {n, 350}] - 1], 10, 111][[1]] (* Robert G. Wilson v, Nov 23 2005 *)
PROG
(PARI) exp(suminf(n=1, (zeta(n+1)-1)/n) - 1) \\ Michel Marcus, May 19 2020
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Eric W. Weisstein, Jun 25 2003
EXTENSIONS
Corrected and extended by Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Jun 24 2003
STATUS
approved