A026119 Bisection of A000016 (also of A000013).

1, 2, 4, 10, 30, 94, 316, 1096, 3856, 13798, 49940, 182362, 671092, 2485534, 9256396, 34636834, 130150588, 490853416, 1857283156, 7048151672, 26817356776, 102280151422, 390937468408, 1497207322930, 5744387279818, 22076468764192

Offset: 0

Author

N. J. A. Sloane, Apr 12 2000

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1666

Crossrefs

Cf. A000013, A000016, A000116.

Bisection of A053634 and A053656.

Programs

PARI

a(n) = sumdiv(2*n+1, d, eulerphi(d)*2^((2*n+1)/d)) / (4*n+2); \\ Michel Marcus, Sep 11 2013

Python

from sympy import totient, divisors
def A026119(n):
    m = (n<<1)+1
    return sum(totient(d)<Chai Wah Wu, Feb 21 2023

Formula

a(n) = (Sum_{d | 2n+1} phi(d)*2^((2n+1)/d)) / (4n+2).