A370746 Decimal expansion of Sum_{k>=1} 1/(k*phi(2*k)), where phi is the Euler totient function (A000010).
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
Offset: 1
Examples
1.76308527715028783029826265318407173005373855503028...
Links
- D. R. Heath-Brown, Cheryl E. Praeger and Aner Shalev, Permutation groups, simple groups, and sieve methods, Isr. J. Math., Vol. 148 (2005), pp. 347-375; alternative link.
- Cheryl E. Praeger, Using the finite simple groups, Gazette of the Australian Mathematical Society, Vol. 38, No. 2 (2011), pp. 93-97.
- Cheryl E. Praeger, Using the finite simple groups, Eureka, Vol. 61 (2011), pp. 64-67 (reprint of the Gazette paper).
- 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).
Programs
-
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]] -
PARI
(4/5)* prodeulerrat(1 + p/((p-1)^2*(p+1)))
Formula
Equals (4/5)* Product_{p prime} (1 + p/((p-1)^2*(p+1))) = (4/5) * A065484.
Comments