A372608 a(n) = Sum_{k=1..n} phi(n*k).

1, 3, 10, 18, 44, 40, 114, 124, 198, 192, 430, 292, 708, 540, 704, 888, 1552, 954, 2178, 1456, 1980, 2080, 3806, 2216, 4220, 3480, 4734, 4056, 7588, 3560, 9270, 6960, 7920, 7840, 9936, 7296, 15588, 10980, 13056, 11120, 21240, 10128, 24570, 16360, 17880, 19360, 32062

Offset: 1

Author

Seiichi Manyama, May 07 2024

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000
• Vaclav Kotesovec, Graph - the asymptotic ratio (100000 terms)
• Eric Weisstein's World of Mathematics, Totient Function.

Crossrefs

Main diagonal of A372606.

Cf. A000010, A070639, A065463.

Programs

Mathematica

Table[Sum[EulerPhi[n*k], {k, 1, n}], {n, 1, 50}] (* Vaclav Kotesovec, Aug 04 2025 *)

PARI

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

Formula

a(n) = A372606(n,n).

a(n) = A000010(n) * A070639(n).

Sum_{k=1..n} a(k) ~ c * n^4, where c = 3*A065463/(4*Pi^2) = 0.053531188209636805... - Vaclav Kotesovec, Aug 04 2025