A169611 - OEIS

%I #21 Jan 16 2022 09:19:11

%S 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,

%T 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,

%U 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

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

%H Reinhard Zumkeller, <a href="/A169611/b169611.txt">Table of n, a(n) for n = 1..10000</a>

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

%F a(n) = A007814(n) + A007949(n). - _R. J. Mathar_, Dec 04 2009

%F a(n) = A001222(A065331(n)). - _Reinhard Zumkeller_, Nov 19 2015

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

%p 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

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

%o (PARI) A169611(n)=valuation(n,2)+valuation(n,3)  \\ _M. F. Hasler_, Aug 24 2012

%o (Haskell)

%o a169611 = a001222 . a065331  -- _Reinhard Zumkeller_, Nov 19 2015

%Y Cf. A001222, A106799.

%Y Cf. A007814, A007949, A065331.

%K nonn

%O 1,4

%A _Juri-Stepan Gerasimov_, Dec 03 2009

%E Definition corrected by _M. F. Hasler_, Aug 24 2012