|
|
A370746
|
|
Decimal expansion of Sum_{k>=1} 1/(k*phi(2*k)), where phi is the Euler totient function (A000010).
|
|
1
|
|
|
1, 7, 6, 3, 0, 8, 5, 2, 7, 7, 1, 5, 0, 2, 8, 7, 8, 3, 0, 2, 9, 8, 2, 6, 2, 6, 5, 3, 1, 8, 4, 0, 7, 1, 7, 3, 0, 0, 5, 3, 7, 3, 8, 5, 5, 5, 0, 3, 0, 2, 8, 6, 9, 0, 7, 3, 3, 6, 3, 9, 6, 4, 3, 5, 8, 9, 7, 3, 3, 5, 0, 9, 4, 4, 9, 4, 8, 2, 1, 5, 6, 3, 9, 8, 0, 5, 8, 1, 2, 8, 3, 3, 5, 2, 1, 1, 1, 6, 5, 0, 0, 2, 9, 1, 0
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
The constant h in Heath-Brown et al. (2005). The asymptotic number of integers n below x which occur as indices of subgroups of nonabelian finite simple groups, excluding that of A_{n-1} in A_n (where A_n is the simple alternating group), is ~ h*x/log(x).
The constant appears in the asymptotic formula for the count of terms of A370745.
|
|
LINKS
|
Cheryl E. Praeger, Using the finite simple groups, Asia Pacific Mathematics Newsletter, Vol. 1, No. 3 (2011), pp. 7-10 (reprint of the Gazette paper).
|
|
FORMULA
|
Equals (4/5)* Product_{p prime} (1 + p/((p-1)^2*(p+1))) = (4/5) * A065484.
|
|
EXAMPLE
|
1.76308527715028783029826265318407173005373855503028...
|
|
MATHEMATICA
|
$MaxExtraPrecision = 500; m = 500; c = LinearRecurrence[{1, 1, -2, 0, 1}, {0, 2, 3, 6, 5}, m]; RealDigits[(4/5)*Exp[NSum[Indexed[c, n]*PrimeZetaP[n]/n, {n, 2, m}, NSumTerms -> m, WorkingPrecision -> m]], 10, 120][[1]]
|
|
PROG
|
(PARI) (4/5)* prodeulerrat(1 + p/((p-1)^2*(p+1)))
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|