A054611 a(n) = Sum_{d|n} phi(d)*4^(n/d).

0, 4, 20, 72, 280, 1040, 4200, 16408, 65840, 262296, 1049680, 4194344, 16782000, 67108912, 268451960, 1073744160, 4295033440, 17179869248, 68719747320, 274877907016, 1099512679520, 4398046544304, 17592190238920, 70368744177752

Offset: 0

Author

N. J. A. Sloane, Apr 16 2000

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1660
• T. Pisanski, D. Schattschneider and B. Servatius, Applying Burnside's lemma to a one-dimensional Escher problem, Math. Mag., 79 (2006), 167-180. See V(n).

Crossrefs

Column k=4 of A185651.

Row n=4 of A054619.

Cf. A001868.

Programs

Maple

A054611:=proc(n) local k, t1; t1:=0; for k in divisors(n) do t1 := t1+phi(k)*4^(n/k); od: t1; end;

PARI

a(n) = if(n==0, 0, sumdiv(n, d, eulerphi(d)*4^(n/d))); \\ Michel Marcus, Sep 19 2017

Formula

a(n) = n * A001868(n).

a(n) = Sum_{k=1..n} 4^gcd(n,k). - Ilya Gutkovskiy, Apr 16 2021