A346622 a(n) = card{ x <= n : x odd and omega(x) = 2 }.
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, 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, 11, 11, 12, 12, 12, 12, 12, 12, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15, 16
Offset: 1
Keywords
Links
- Chai Wah Wu, Table of n, a(n) for n = 1..10000
Programs
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Maple
a:= proc(n) option remember; `if`(n=0, 0, a(n-1)+ `if`(n::odd and nops(ifactors(n)[2])=2, 1, 0)) end: seq(a(n), n=1..87); # Alois P. Heinz, Aug 23 2021 -
Mathematica
a[n_] := a[n] = If[n==0, 0, a[n-1]+If[OddQ[n] && PrimeNu[n]==2, 1, 0]]; Table[a[n], {n, 1, 87}] (* Jean-François Alcover, Apr 07 2022 *) 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 *) -
Python
from sympy import primefactors def A346622(n): 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