cp's OEIS Frontend

A249141 Decimal expansion of 'sigma', a constant associated with the expected number of random elements to generate a finite abelian group.

%I A249141 #16 Jan 17 2020 16:21:57
%S A249141 2,1,1,8,4,5,6,5,6,3,4,7,0,1,6,3,5,3,2,3,8,2,5,2,7,7,6,9,1,0,2,3,6,4,
%T A249141 7,6,4,2,8,8,5,9,0,7,8,5,6,1,8,5,1,7,9,1,5,4,1,4,2,6,3,8,5,2,9,0,9,8,
%U A249141 3,4,1,1,2,3,6,5,3,4,6,3,4,5,7,7,5,5,7,0,8,2,5,9,7,8,1,8,7,6,7,9,3,9
%N A249141 Decimal expansion of 'sigma', a constant associated with the expected number of random elements to generate a finite abelian group.
%D A249141 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.1 Abelian group enumeration constants, p. 273.
%H A249141 Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants</a>, p. 33.
%H A249141 Carl Pomerance, <a href="https://math.dartmouth.edu/~carlp/PDF/paper123.pdf">The expected number of random elements to generate a finite abelian group</a>, Periodica Mathematica Hungarica 43 (2001), 191-198.
%F A249141 sigma = 1+sum_{j >= 2} (1-prod_{k >= j} zeta(k)^(-1)).
%e A249141 2.11845656347016353238252776910236476428859...
%t A249141 digits = 102; jmax = 400; P[j_] := 1/Product[N[Zeta[k], digits+100], {k, j, jmax}]; sigma = 1+Sum[1 - P[j], {j, 2, jmax}]; RealDigits[sigma, 10, digits] // First
%o A249141 (PARI) default(realprecision,120); 1 + suminf(j=2, 1 - prodinf(k=j, 1/zeta(k))) \\ _Michel Marcus_, Oct 22 2014
%Y A249141 Cf. A021002, A033150, A084892, A084893.
%K A249141 nonn,cons
%O A249141 1,1
%A A249141 _Jean-François Alcover_, Oct 22 2014