A001226 Lerch's function q_2(n) = (2^{phi(t)} - 1)/t where t = 2*n - 1.

1, 1, 3, 9, 7, 93, 315, 17, 3855, 13797, 195, 182361, 41943, 9709, 9256395, 34636833, 31775, 479349, 1857283155, 430185, 26817356775, 102280151421, 372827, 1497207322929, 89756051247, 84215045, 84973577874915, 19991120505, 1205604855, 4885260612740877

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Lerch defines q_u = (u^phi(p) - 1)/p for any odd integer p and for u prime to p. - Altug Alkan, Dec 19 2017

References

• L. E. Dickson, History of the Theory of Numbers. Carnegie Institute Public. 256, Washington, DC, Vol. 1, 1919; Vol. 2, 1920; Vol. 3, 1923, see vol. 1, p. 109.

Links

• T. D. Noe, Table of n, a(n) for n = 1..200
• R. C. Read, Letter to N. J. A. Sloane, Oct. 29, 1976

Crossrefs

Cf. A000010.

Programs

Mathematica

Table[(2^EulerPhi[n] - 1)/n, {n, 1, 40, 2}] (* T. D. Noe, Jun 26 2012 *)

PARI

a(n) = (2^eulerphi(2*n-1) - 1)/(2*n-1) \\ Andrew Howroyd, Dec 18 2017