OFFSET
1,2
FORMULA
G.f.: Sum_{k >= 1} phi(k) * x^k/(1 - x^k)^(k+1).
If p is prime, a(p) = 2*p - 1.
From Richard L. Ollerton, May 07 2021: (Start)
a(n) = Sum_{k=1..n} binomial(gcd(n,k) + n/gcd(n,k) - 1,n/gcd(n,k)).
a(n) = Sum_{k=1..n} binomial(gcd(n,k) + n/gcd(n,k) - 1,gcd(n,k))*phi(gcd(n,k))/phi(n/gcd(n,k)). (End)
MATHEMATICA
a[n_] := DivisorSum[n, EulerPhi[#] * Binomial[# + n/# - 1, #] &]; Array[a, 100] (* Amiram Eldar, Apr 22 2021 *)
PROG
(PARI) a(n) = sumdiv(n, d, eulerphi(d)*binomial(d+n/d-1, d));
(PARI) my(N=66, x='x+O('x^N)); Vec(sum(k=1, N, eulerphi(k)*x^k/(1-x^k)^(k+1)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 22 2021
STATUS
approved