A169611 Number of prime divisors of n that are not greater than 3, counted with multiplicity.

0, 1, 1, 2, 0, 2, 0, 3, 2, 1, 0, 3, 0, 1, 1, 4, 0, 3, 0, 2, 1, 1, 0, 4, 0, 1, 3, 2, 0, 2, 0, 5, 1, 1, 0, 4, 0, 1, 1, 3, 0, 2, 0, 2, 2, 1, 0, 5, 0, 1, 1, 2, 0, 4, 0, 3, 1, 1, 0, 3, 0, 1, 2, 6, 0, 2, 0, 2, 1, 1, 0, 5, 0, 1, 1, 2, 0, 2, 0, 4, 4, 1, 0, 3, 0, 1, 1, 3, 0, 3, 0, 2, 1, 1, 0, 6, 0, 1, 2, 2, 0, 2, 0, 3, 1

Offset: 1

Author

Juri-Stepan Gerasimov, Dec 03 2009

Keywords

• nonn

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001222, A106799.

Cf. A007814, A007949, A065331.

Programs

Haskell

a169611 = a001222 . a065331  -- Reinhard Zumkeller, Nov 19 2015

Maple

A169611 := proc(n) local f; a := 0 ; for f in ifactors(n)[2] do if op(1,f) <= 3 then a := a+op(2,f) ; end if; end do: return a; end proc: seq(A169611(n),n=1..100) ; # R. J. Mathar, Dec 04 2009

Mathematica

f[n_] := Plus @@ Last /@ Select[ FactorInteger@ n, 1 < #[[1]] < 4 &]; Array[f, 105] (* Robert G. Wilson v, Dec 19 2009 *)

PARI

A169611(n)=valuation(n,2)+valuation(n,3)  \\ M. F. Hasler, Aug 24 2012

Formula

a(n) = A001222(n) - A106799(n).

a(n) = A007814(n) + A007949(n). - R. J. Mathar, Dec 04 2009

a(n) = A001222(A065331(n)). - Reinhard Zumkeller, Nov 19 2015

Asymptotic mean: lim_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 3/2. - Amiram Eldar, Jan 16 2022

Extensions

Definition corrected by M. F. Hasler, Aug 24 2012