A369779 a(n) = n * Sum_{p|n, p prime} phi(n/p) / p.

0, 1, 1, 2, 1, 8, 1, 8, 6, 22, 1, 20, 1, 44, 26, 32, 1, 66, 1, 48, 48, 112, 1, 80, 20, 158, 54, 92, 1, 172, 1, 128, 116, 274, 62, 156, 1, 344, 162, 192, 1, 348, 1, 228, 174, 508, 1, 320, 42, 540, 278, 320, 1, 594, 130, 368, 348, 814, 1, 448, 1, 932, 306, 512, 176

Offset: 1

Author

Wesley Ivan Hurt, Jan 31 2024

Keywords

• nonn
• easy

Comments

Dirichlet convolution of A010051(n) and A002618(n). - Wesley Ivan Hurt, Jul 10 2025

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A000010, A002618, A010051, A057660, A117494, A347104, A369687.

Cf. also A369894, A369907, A369909.

Programs

Mathematica

Table[n*DivisorSum[n, EulerPhi[n/#]/# &, PrimeQ[#] &], {n, 100}]

PARI

A369779(n) = if(1==n, 0, my(f=factor(n)); n*sum(i=1, #f~, (eulerphi(n/f[i, 1])/f[i,1]))); \\ Antti Karttunen, Jan 23 2025

Formula

From Wesley Ivan Hurt, Jul 10 2025: (Start)

a(n) = Sum_{d|n} A010051(d) * A002618(n/d).

a(p^k) = ceiling(p^(2k-2)-p^(2k-3)) for p prime and k>=1. (End)