A346622 - OEIS

%I #14 Oct 05 2022 13:40:42

%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,

%T 4,4,4,4,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,8,8,9,9,9,9,9,9,10,10,11,11,

%U 11,11,12,12,12,12,12,12,13,13,14,14,14,14,14,14,14,14,15,15,16

%N a(n) = card{ x <= n : x odd and omega(x) = 2 }.

%H Chai Wah Wu, <a href="/A346622/b346622.txt">Table of n, a(n) for n = 1..10000</a>

%p a:= proc(n) option remember; `if`(n=0, 0, a(n-1)+

%p      `if`(n::odd and nops(ifactors(n)[2])=2, 1, 0))

%p     end:

%p seq(a(n), n=1..87);  # _Alois P. Heinz_, Aug 23 2021

%t a[n_] := a[n] = If[n==0, 0, a[n-1]+If[OddQ[n] && PrimeNu[n]==2, 1, 0]];

%t Table[a[n], {n, 1, 87}] (* _Jean-François Alcover_, Apr 07 2022 *)

%t nxt[{n_,a_}]:={n+1,If[EvenQ[n]&&PrimeNu[n+1]==2,1,0]+a}; NestList[nxt,{1,0},90][[All,2]] (* _Harvey P. Dale_, Oct 05 2022 *)

%o (Python)

%o from sympy import primefactors

%o def A346622(n):

%o     return 0 if n <= 2 else A346622(n-1) + (1 if n % 2 and len(primefactors(n)) == 2 else 0) # _Chai Wah Wu_, Aug 23 2021

%Y Cf. A007774, A082997, A146167, A346623.

%K nonn

%O 1,21

%A _N. J. A. Sloane_, Aug 23 2021