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A344523
a(n) = Sum_{1 <= i, j, k, l <= n} gcd(i,j,k,l).
6
1, 17, 84, 276, 649, 1417, 2528, 4432, 7033, 10905, 15556, 22836, 30673, 41729, 54944, 71968, 89969, 115457, 140820, 175444, 212537, 257113, 302720, 366160, 426505, 500873, 580676, 677108, 769761, 895377, 1008928, 1153120, 1300417, 1469073, 1640020, 1860340, 2054921
OFFSET
1,2
LINKS
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
Column k=4 of A344479.
Sequence in context: A197346 A213436 A239667 * A156968 A212487 A288420
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 22 2021
STATUS
approved