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

1,4

Links

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

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

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 *)

Prog

(PARI) A169611(n)=valuation(n, 2)+valuation(n, 3)  \\ M. F. Hasler, Aug 24 2012
(Haskell)
a169611 = a001222 . a065331  -- Reinhard Zumkeller, Nov 19 2015

Crossrefs

Cf. A001222, A106799.

Cf. A007814, A007949, A065331.

Sequence in context: A273846 A090290 A153585 * A242460 A144494 A136166

Adjacent sequences: A169608 A169609 A169610 * A169612 A169613 A169614

Keyword

nonn

Author

Juri-Stepan Gerasimov, Dec 03 2009

Extensions

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

Status

approved