A021002 - OEIS

A021002

Decimal expansion of zeta(2)*zeta(3)*zeta(4)*...

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

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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

Robert Price, Table of n, a(n) for n = 1..1000

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.

Feihu Liu, Sihao Tao, and Guoce Xin, Unimodular Equivalence of Integral Simplices, arXiv:2601.06819 [math.CO], 2026. See p. 21, Lemma 4.4.

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.

Index entries for constants related to zeta

FORMULA

Product of A080729 and A080730. - R. J. Mathar, Feb 16 2011

EXAMPLE

2.2948565916733137941835158313443112887131637994416686732758140300...

MAPLE

evalf(product(Zeta(n), n=2..infinity), 200);

MATHEMATICA