A385313 a(n) = c(n) + Sum_{d|n} d * phi(n/d) * (1 - c(d)), where c = A010051.

1, 2, 3, 6, 5, 8, 7, 16, 15, 14, 11, 30, 13, 20, 23, 40, 17, 45, 19, 54, 33, 32, 23, 80, 45, 38, 63, 78, 29, 97, 31, 96, 53, 50, 59, 144, 37, 56, 63, 144, 41, 139, 43, 126, 135, 68, 47, 200, 91, 135, 83, 150, 53, 189, 95, 208, 93, 86, 59, 300, 61, 92, 195, 224, 113, 223, 67, 198, 113, 245, 71, 372, 73, 110, 225, 222, 137, 265, 79, 360, 243, 122, 83, 432

Offset

1,2

Comments

Möbius transform of A380447.

Links

Table of n, a(n) for n=1..84.

Formula

a(n) = Sum_{d|n} A380447(d) * mu(n/d).

a(p^k) = (1-k+k*p)*p^(k-1) for p prime, k>=1. - Wesley Ivan Hurt, Jul 02 2025

Mathematica

Table[(PrimePi[n] - PrimePi[n - 1]) + Sum[d*EulerPhi[n/d] (1 - (PrimePi[d] - PrimePi[d - 1])), {d, Divisors[n]}], {n, 100}]

Crossrefs

Cf. A000010 (phi), A010051, A018804, A380447.

Sequence in context: A048750 A344403 A326136 * A276081 A329564 A257011

Adjacent sequences: A385310 A385311 A385312 * A385314 A385315 A385316

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 25 2025

Status

approved