A333291 a(n) = Sum_{i=1..n, gcd(i,n)=1} i*phi(i) where phi is Euler's totient function A000010.

1, 1, 3, 7, 17, 21, 49, 69, 105, 103, 217, 173, 375, 347, 435, 509, 863, 601, 1243, 983, 1271, 1265, 2217, 1449, 2575, 2225, 2935, 2573, 4549, 2241, 5601, 4609, 5195, 4997, 6453, 4531, 9519, 7099, 8457, 6897, 13111, 6621, 15255, 11053, 11691, 12397, 20033, 11471, 20905, 14563, 19307, 17663, 28901, 16285, 26119

Offset: 1

Author

N. J. A. Sloane, Mar 22 2020

Keywords

• nonn
• look

Links

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

Crossrefs

Suggested by A023896 and A319087.

Cf. A000010, A011755.

Programs

Maple

a:= n-> add(`if`(igcd(i, n)=1, i*numtheory[phi](i), 0), i=1..n):
seq(a(n), n=1..55);  # Alois P. Heinz, Mar 22 2020

Mathematica

a[n_] := Sum[If[CoprimeQ[i, n], i * EulerPhi[i], 0], {i, 1, n}]; Array[a, 100] (* Amiram Eldar, Dec 01 2024 *)

PARI

a(n) = sum(i=1, n, if (gcd(n, i) == 1, i*eulerphi(i))); \\ Michel Marcus, Mar 23 2020