OFFSET
1,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = Sum_{k=1..n} phi(k) * floor(n/k)^4.
G.f.: (1/(1 - x)) * Sum_{k >= 1} phi(k) * x^k * (1 + 11*x^k + 11*x^(2*k) + x^(3*k))/(1 - x^k)^4.
a(n) ~ 90 * zeta(3) * n^4 / Pi^4. - Vaclav Kotesovec, May 23 2021
MATHEMATICA
a[n_] := Sum[EulerPhi[k] * Quotient[n, k]^4, {k, 1, n}]; Array[a, 50] (* Amiram Eldar, May 22 2021 *)
PROG
(PARI) a(n) = sum(i=1, n, sum(j=1, n, sum(k=1, n, sum(l=1, n, gcd([i, j, k, l])))));
(PARI) a(n) = sum(k=1, n, eulerphi(k)*(n\k)^4);
(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, eulerphi(k)*x^k*(1+11*x^k+11*x^(2*k)+x^(3*k))/(1-x^k)^4)/(1-x))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 22 2021
STATUS
approved