OFFSET
1,1
COMMENTS
A very good approximation is 2e-Pi = ~2.29497100332829723225793155942... - Marco Matosic, Nov 16 2005
This constant is equal to the asymptotic mean of number of Abelian groups of order n (A000688). - Amiram Eldar, Oct 16 2020
REFERENCES
R. Ayoub, An Introduction to the Analytic Theory of Numbers, Amer. Math. Soc., 1963, p. 198-9.
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.1 Abelian group enumeration constants, p. 274.
LINKS
Steven R. Finch, Abelian Group Enumeration Constants. [From the Wayback machine]
Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 86.
Felix Fontein and Pawel Wocjan, Quantum Algorithm for Computing the Period Lattice of an Infrastructure, arXiv preprint arXiv:1111.1348 [quant-ph], 2011.
Felix Fontein and Pawel Wocjan, On the probability of generating a lattice, Journal of Symbolic Computation, Vol. 64 (2014), pp. 3-15, arXiv preprint, arXiv:1211.6246 [math.CO], 2012-2013. - From N. J. A. Sloane, Jan 03 2013
Bernd C. Kellner, On asymptotic constants related to products of Bernoulli numbers and factorials, Integers, Vol. 9 (2009), Article #A08, pp. 83-106; alternative link; arXiv:0604505 [math.NT], 2006.
B. R. Srinivasan, On the Number of Abelian Groups of a Given Order, Acta Arithmetica, Vol. 23, No. 2 (1973), pp. 195-205, alternative link.
Eric Weisstein's World of Mathematics, Abelian Group.
FORMULA
EXAMPLE
2.2948565916733137941835158313443112887131637994416686732758140300...
MAPLE
evalf(product(Zeta(n), n=2..infinity), 200);
MATHEMATICA
p = Product[ N[ Zeta[n], 256], {n, 2, 1000}]; RealDigits[p, 10, 111][[1]] (* Robert G. Wilson v, Nov 22 2005 *)
PROG
(PARI) prodinf(n=2, zeta(n)) \\ Charles R Greathouse IV, May 27 2015
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
Andre Neumann Kauffman (ank(AT)nlink.com.br)
EXTENSIONS
More terms from Simon Plouffe, Jan 07 2002
Further terms from Robert G. Wilson v, Nov 22 2005
Mathematica program fixed by Vaclav Kotesovec, Sep 20 2014
STATUS
approved