A069812 a(n) = Sum_{k=1..n} (bigomega(k)-omega(k)).

0, 0, 0, 1, 1, 1, 1, 3, 4, 4, 4, 5, 5, 5, 5, 8, 8, 9, 9, 10, 10, 10, 10, 12, 13, 13, 15, 16, 16, 16, 16, 20, 20, 20, 20, 22, 22, 22, 22, 24, 24, 24, 24, 25, 26, 26, 26, 29, 30, 31, 31, 32, 32, 34, 34, 36, 36, 36, 36, 37, 37, 37, 38, 43, 43, 43, 43, 44, 44, 44, 44, 47, 47, 47, 48

Offset: 1

Author

Benoit Cloitre, Apr 30 2002

Keywords

• easy
• nonn

Links

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

Crossrefs

Cf. A001221, A001222, A046660, A136141.

Programs

Mathematica

Accumulate[Table[PrimeOmega[n]-PrimeNu[n],{n,80}]] (* Harvey P. Dale, Oct 10 2015 *)

PARI

lista(nmax) = {my(s = 0, e); for(n = 1, nmax, e = factor(n)[, 2]; s += vecsum(e) - #e; print1(s, ", "));} \\ Amiram Eldar, Sep 17 2024

Formula

a(n) ~ A136141 * n, where A136141 = 0.773156669... - Vaclav Kotesovec, Sep 01 2019

G.f.: (1/(1 - x)) * Sum_{p prime, k>=2} x^(p^k)/(1 - x^(p^k)). - Ilya Gutkovskiy, Sep 03 2019