OFFSET
1,2
FORMULA
a(n) = Sum_{d|n} phi(d^(d+1)) = Sum_{d|n} phi(d) * d^d.
G.f.: Sum_{k>=1} phi(k^(k+1))*x^k/(1 - x^k).
MATHEMATICA
a[n_] := Sum[(n/GCD[k, n])^(n/GCD[k, n]), {k, 1, n}]; Array[a, 20] (* Amiram Eldar, Mar 11 2021 *)
PROG
(PARI) a(n) = sum(k=1, n, (n/gcd(k, n))^(n/gcd(k, n)));
(PARI) a(n) = sumdiv(n, d, eulerphi(d^(d+1)));
(PARI) a(n) = sumdiv(n, d, eulerphi(d)*d^d);
(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, eulerphi(k^(k+1))*x^k/(1-x^k)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 11 2021
STATUS
approved