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

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

Offset

1,1

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.1 Abelian group enumeration constants, p. 273.

Links

Table of n, a(n) for n=1..102.

Steven R. Finch, Errata and Addenda to Mathematical Constants, p. 33.

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 * A353953 A102875 A329070

Adjacent sequences: A249138 A249139 A249140 * A249142 A249143 A249144

Keyword

nonn,cons

Author

Jean-François Alcover, Oct 22 2014

Status

approved