A344139 a(n) = Sum_{x_1|n, x_2|n, x_3|n, x_4|n, x_5|n} gcd(x_1,x_2,x_3,x_4,x_5).

1, 33, 34, 277, 36, 1122, 38, 1335, 313, 1188, 42, 9418, 44, 1254, 1224, 4771, 48, 10329, 50, 9972, 1292, 1386, 54, 45390, 391, 1452, 1720, 10526, 60, 40392, 62, 14193, 1428, 1584, 1368, 86701, 68, 1650, 1496, 48060, 72, 42636, 74, 11634, 11268, 1782, 78, 162214, 477, 12903, 1632, 12188, 84

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Formula

a(n) = Sum_{x_1|n, x_2|n, x_3|n, x_4|n, x_5|n} n/lcm(x_1,x_2,x_3,x_4,x_5).

a(n) = Sum_{d|n} phi(n/d) * tau(d)^5.

If p is prime, a(p) = 31 + p.

a(n) = Sum_{k=1..n} tau(gcd(k,n))^5.

Mathematica

a[n_] := DivisorSum[n, EulerPhi[n/#] * DivisorSigma[0, #]^5 &]; Array[a, 20] (* Amiram Eldar, May 10 2021 *)

Prog

(PARI) a(n) = sumdiv(n, i, sumdiv(n, j, sumdiv(n, k, sumdiv(n, l, sumdiv(n, m, gcd([i, j, k, l, m]))))));
(PARI) a(n) = sumdiv(n, i, sumdiv(n, j, sumdiv(n, k, sumdiv(n, l, sumdiv(n, m, n/lcm([i, j, k, l, m]))))));
(PARI) a(n) = sumdiv(n, d, eulerphi(n/d)*numdiv(d)^5);
(PARI) a(n) = sum(k=1, n, numdiv(gcd(k, n))^5);

Crossrefs

Cf. A000203, A060724, A344132, A344138, A344140.

Sequence in context: A335072 A260678 A329658 * A140143 A041543 A144425

Adjacent sequences: A344136 A344137 A344138 * A344140 A344141 A344142

Keyword

nonn,mult

Author

Seiichi Manyama, May 10 2021

Status

approved