A343520 a(n) = Sum_{1 <= x_1 <= x_2 <= x_3 <= x_4 <= x_5 <= x_6 <= n} gcd(x_1, x_2, x_3 , x_4, x_5, x_6, n).

1, 8, 30, 93, 214, 506, 930, 1818, 3065, 5247, 8018, 13080, 18576, 28104, 39300, 56184, 74629, 104978, 134614, 182897, 232258, 304098, 376762, 492068, 594635, 754941, 912384, 1137106, 1344932, 1674374, 1947822, 2382888, 2776997, 3337364, 3843360, 4629687, 5245822, 6231194

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+5, 6).

G.f.: Sum_{k >= 1} phi(k) * x^k/(1 - x^k)^7.

Sum_{k=1..n} a(k) ~ Pi^6 * n^7 / (4762800*zeta(7)). - Vaclav Kotesovec, May 23 2021

Mathematica

a[n_] := DivisorSum[n, EulerPhi[n/#] * Binomial[# + 5, 6] &]; Array[a, 50] (* Amiram Eldar, Apr 18 2021 *)

Prog

(PARI) a(n) = sumdiv(n, d, eulerphi(n/d)*binomial(d+5, 6));
(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, eulerphi(k)*x^k/(1-x^k)^7))

Crossrefs

Column 6 of A343516.

Cf. A000010, A343508.

Sequence in context: A232772 A213776 A113751 * A107233 A098213 A163613

Adjacent sequences: A343517 A343518 A343519 * A343521 A343522 A343523

Keyword

nonn

Author

Seiichi Manyama, Apr 17 2021

Status

approved