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

1,21

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

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 *)

Prog

(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

Crossrefs

Cf. A007774, A082997, A146167, A346623.

Sequence in context: A082996 A094382 A146167 * A103380 A309120 A098708

Adjacent sequences: A346619 A346620 A346621 * A346623 A346624 A346625

Keyword

nonn

Author

N. J. A. Sloane, Aug 23 2021

Status

approved