OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..200
FORMULA
a(n) = Sum_{k=1..n} n^gcd(k,n) = n * A056665(n). - Seiichi Manyama, Mar 10 2021
a(n) = Sum_{k=1..n} n^(n/gcd(n,k))*phi(gcd(n,k))/phi(n/gcd(n,k)). - Richard L. Ollerton, May 07 2021
MAPLE
with(numtheory):
a:= n-> add(phi(d)*n^(n/d), d=divisors(n)):
seq(a(n), n=0..20);
MATHEMATICA
a[0] = 0; a[n_] := DivisorSum[n, EulerPhi[#]*n^(n/#)&]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Mar 21 2017 *)
PROG
(Python)
from sympy import totient, divisors
def A228640(n):
return sum(totient(d)*n**(n//d) for d in divisors(n, generator=True)) # Chai Wah Wu, Feb 15 2020
(PARI) a(n) = if (n, sumdiv(n, d, eulerphi(d)*n^(n/d)), 0); \\ Michel Marcus, Feb 15 2020; corrected Jun 13 2022
(PARI) a(n) = sum(k=1, n, n^gcd(k, n)); \\ Seiichi Manyama, Mar 10 2021
(Magma) [0] cat [&+[EulerPhi(d)*n^(n div d): d in Divisors(n)]:n in [1..20]]; // Marius A. Burtea, Feb 15 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 28 2013
STATUS
approved