OFFSET
1,2
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 1..10000
FORMULA
From Vaclav Kotesovec, Jun 05 2021: (Start)
a(n) ~ Pi^2 * n^3 / (36*zeta(3)).
G.f.: 1/(1-x) * Sum_{k>=1} phi(k) * x^k/(1 - x^k)^3, where phi is the Euler totient function (A000010).
a(n) = Sum_{k=1..n} Sum_{d|k} phi(k/d) * d*(d+1)/2. (End)
a(n) = Sum_{k=1..n} phi(k) * binomial(floor(n/k)+2,3). - Seiichi Manyama, Sep 13 2024
MATHEMATICA
a[n_] := Sum[Sum[Sum[GCD[i, j, k], {i, 1, j}], {j, 1, k}], {k, 1, n}]; Array[a, 50] (* Amiram Eldar, May 25 2021 *)
nmax = 100; Rest[CoefficientList[Series[1/(1 - x)*Sum[EulerPhi[k]*x^k/(1 - x^k)^3, {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Jun 05 2021 *)
Accumulate[Table[Sum[EulerPhi[n/d] * d*(d+1)/2, {d, Divisors[n]}], {n, 1, 100}]] (* Vaclav Kotesovec, Jun 05 2021 *)
PROG
(PARI) a(n) = sum(i=1, n, sum(j=i, n, sum(k=j, n, gcd([i, j, k]))));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 22 2021
STATUS
approved