A372636 a(n) = Sum_{j=1..n} Sum_{k=1..n} phi(j*k) / phi(k).

1, 5, 14, 31, 58, 93, 148, 219, 306, 407, 550, 695, 898, 1103, 1323, 1610, 1963, 2293, 2738, 3152, 3597, 4116, 4773, 5362, 6073, 6808, 7611, 8437, 9492, 10348, 11557, 12728, 13868, 15143, 16425, 17753, 19482, 21083, 22687, 24350, 26481, 28186, 30535, 32641

Offset: 1

Author

Seiichi Manyama, May 08 2024

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..10000
• Vaclav Kotesovec, Plot of a(n)/n^3 for n = 1..10000
• Eric Weisstein's World of Mathematics, Totient Function.

Crossrefs

Cf. A330596, A372619, A372633.

Programs

Mathematica

Table[Sum[Sum[EulerPhi[j*k], {j, 1, n}] / EulerPhi[k], {k, 1, n}], {n, 1, 50}] (* Vaclav Kotesovec, May 08 2024 *)
s = 1; Join[{1}, Table[s += Sum[EulerPhi[j*n] / EulerPhi[j], {j, 1, n}] + Sum[EulerPhi[j*n], {j, 1, n-1}] / EulerPhi[n], {n, 2, 50}]] (* Vaclav Kotesovec, May 08 2024 *)

PARI

a(n) = sum(j=1, n, sum(k=1, n, eulerphi(j*k)/eulerphi(k)));

Formula

a(n) ~ c * n^3, where c = A330596 / 2 = 0.374267629841... . - Amiram Eldar, May 09 2024