login
A169611
Number of prime divisors of n that are not greater than 3, counted with multiplicity.
12
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
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
KEYWORD
nonn
AUTHOR
EXTENSIONS
Definition corrected by M. F. Hasler, Aug 24 2012
STATUS
approved