OFFSET
1,2
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = Sum_{d|n} phi(n/d) * binomial(d+3, 4).
G.f.: Sum_{k >= 1} phi(k) * x^k/(1 - x^k)^5.
Sum_{k=1..n} a(k) ~ Pi^4 * n^5 / (10800*zeta(5)). - Vaclav Kotesovec, May 23 2021
MATHEMATICA
a[n_] := DivisorSum[n, EulerPhi[n/#] * Binomial[# + 3, 4] &]; Array[a, 50] (* Amiram Eldar, Apr 18 2021 *)
PROG
(PARI) a(n) = sum(a=1, n, sum(b=1, a, sum(c=1, b, sum(d=1, c, gcd(gcd(gcd(gcd(n, a), b), c), d)))));
(PARI) a(n) = sumdiv(n, d, eulerphi(n/d)*binomial(d+3, 4));
(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, eulerphi(k)*x^k/(1-x^k)^5))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 17 2021
STATUS
approved