OFFSET
1,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..5000
FORMULA
G.f.: Sum_{k>=1} phi(k)*x^k/(1 - phi(k)*x^k).
L.g.f.: -log(Product_{k>=1} (1 - phi(k)*x^k)^(1/k)).
a(p) = p for p prime.
a(n) = Sum_{k=1..n} phi(n/gcd(k, n))^(gcd(k, n) - 1). - Seiichi Manyama, Mar 13 2021
MATHEMATICA
Table[Sum[EulerPhi[n/d]^d, {d, Divisors[n]}], {n, 1, 55}]
nmax = 55; CoefficientList[Series[Sum[EulerPhi[k] x^k/(1 - EulerPhi[k] x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
nmax = 55; CoefficientList[Series[-Log[Product[(1 - EulerPhi[k] x^k)^(1/k), {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax] // Rest
PROG
(PARI) a(n) = sum(k=1, n, eulerphi(n/gcd(k, n))^(gcd(k, n)-1)); \\ Seiichi Manyama, Mar 13 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jul 25 2019
STATUS
approved