A333699 a(n) = Sum_{d|n} phi(n/d) * pi(d).
0, 1, 2, 3, 3, 7, 4, 8, 8, 11, 5, 18, 6, 16, 20, 18, 7, 27, 8, 30, 28, 23, 9, 44, 21, 27, 29, 41, 10, 58, 11, 41, 41, 34, 45, 68, 12, 38, 48, 72, 13, 83, 14, 62, 76, 45, 15, 98, 39, 72, 61, 72, 16, 95, 66, 101, 68, 54, 17, 147, 18, 59, 106, 89, 78, 125, 19, 92, 81, 136
Offset: 1
Keywords
Programs
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Mathematica
Table[Sum[EulerPhi[n/d] PrimePi[d], {d, Divisors[n]}], {n, 70}] Table[Sum[PrimePi[GCD[n, k]], {k, n}], {n, 70}] -
PARI
a(n) = sumdiv(n, d, eulerphi(n/d)*primepi(d)); \\ Michel Marcus, Apr 03 2020
Formula
G.f.: Sum_{k>=1} Sum_{j>=1} phi(j) * x^(j*prime(k)) / (1 - x^j).
a(n) = Sum_{k=1..n} pi(gcd(n,k)).
a(n) = Sum_{d|n} A386596(d) * mu(n/d). - Wesley Ivan Hurt, Jul 26 2025
Comments