OFFSET
1,2
FORMULA
Sum_{k=1..n} a(k) = A344522(n).
G.f.: Sum_{k >= 1} phi(k) * x^k * (1 + 4*x^k + x^(2*k))/(1 - x^k)^3.
MATHEMATICA
a[n_] := Sum[EulerPhi[k] * First @ Differences @ (Quotient[{n - 1, n}, k]^3), {k, 1, n}]; Array[a, 40] (* Amiram Eldar, May 24 2021 *)
PROG
(PARI) a(n) = sum(k=1, n, eulerphi(k)*((n\k)^3-((n-1)\k)^3));
(PARI) my(N=66, x='x+O('x^N)); Vec(sum(k=1, N, eulerphi(k)*x^k*(1+4*x^k+x^(2*k))/(1-x^k)^3))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 24 2021
STATUS
approved