A372633 a(n) = Sum_{j=1..n} Sum_{k=1..n} phi(j*k).

1, 5, 19, 47, 115, 183, 369, 585, 927, 1271, 2021, 2557, 3817, 4813, 6101, 7749, 10581, 12381, 16395, 19147, 22855, 26795, 33901, 38141, 46081, 52729, 61711, 69487, 83851, 90731, 108341, 121749, 136929, 152065, 171097, 185257, 215101, 236377, 261553, 283153, 323993

Offset

1,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..10000

Vaclav Kotesovec, Plot of a(n)/n^4 for n = 1..100000

Eric Weisstein's World of Mathematics, Totient Function.

Formula

a(n) ~ c * n^4, where c = A065464 / 4 = 0.107062376419... . - Amiram Eldar, May 09 2024

Mathematica

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

Prog

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

Crossrefs

Cf. A000010, A002088, A057434, A065464, A372606, A372635.

Sequence in context: A243895 A024191 A277801 * A328191 A100104 A015650

Adjacent sequences: A372630 A372631 A372632 * A372634 A372635 A372636

Keyword

nonn,nice

Author

Seiichi Manyama, May 08 2024

Status

approved