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 A249141 Decimal expansion of 'sigma', a constant associated with the expected number of random elements to generate a finite abelian group. 1
 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, 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, 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 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 REFERENCES Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.1 Abelian group enumeration constants, p. 273. LINKS Steven R. Finch, Errata and Addenda to Mathematical Constants, p. 33. Steven R. Finch, Errata and Addenda to Mathematical Constants, January 22, 2016. [Cached copy, with permission of the author] Carl Pomerance, The expected number of random elements to generate a finite abelian group, Periodica Mathematica Hungarica 43 (2001), 191-198. FORMULA sigma = 1+sum_{j >= 2} (1-prod_{k >= j} zeta(k)^(-1)). EXAMPLE 2.11845656347016353238252776910236476428859... MATHEMATICA 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 PROG (PARI) default(realprecision, 120); 1 + suminf(j=2, 1 - prodinf(k=j, 1/zeta(k))) \\ Michel Marcus, Oct 22 2014 CROSSREFS Cf. A021002, A033150, A084892, A084893. Sequence in context: A053373 A297733 A255812 * A102875 A157785 A021476 Adjacent sequences:  A249138 A249139 A249140 * A249142 A249143 A249144 KEYWORD nonn,cons,changed AUTHOR Jean-François Alcover, Oct 22 2014 STATUS approved

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Last modified April 24 12:01 EDT 2019. Contains 322429 sequences. (Running on oeis4.)