A046470 Even numbers with an odd number of prime factors (counted with multiplicity).

2, 8, 12, 18, 20, 28, 30, 32, 42, 44, 48, 50, 52, 66, 68, 70, 72, 76, 78, 80, 92, 98, 102, 108, 110, 112, 114, 116, 120, 124, 128, 130, 138, 148, 154, 162, 164, 168, 170, 172, 174, 176, 180, 182, 186, 188, 190, 192, 200, 208, 212, 222, 230, 236, 238, 242, 244

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(2)=8, which is even with odd number of prime factors i.e. 3.

Maple

filter:= proc(n) numtheory:-bigomega(n) mod 2 = 1 end proc:
select(filter, [seq(i, i=2..1000, 2)]); # Robert Israel, Apr 02 2025

Mathematica

Select[Range[2, 244, 2], OddQ[PrimeOmega[#]] &] (* Jayanta Basu, Jun 26 2013 *)

Prog

(Python)
from math import isqrt, prod
from sympy import primerange, integer_nthroot, primepi
from oeis_sequences.OEISsequences import bisection
def A046470(n):
    def g(x, a, b, c, m): yield from (((d, ) for d in enumerate(primerange(b, isqrt(x//c)+1), a)) if m==2 else (((a2, b2), )+d for a2, b2 in enumerate(primerange(b, integer_nthroot(x//c, m)[0]+1), a) for d in g(x, a2, b2, c*b2, m-1)))
    def f(x): return int(n+x-1-sum(sum(primepi((x>>1)//prod(c[1] for c in a))-a[-1][0] for a in g(x>>1, 0, 1, 1, m)) for m in range(2, x.bit_length(), 2)))
    return bisection(f, n+1, n+1) # Chai Wah Wu, Dec 19 2025

Crossrefs

Cf. A046337. Intersection of A005843 and A026424.

Sequence in context: A290608 A340690 A303900 * A388980 A090772 A046525

Adjacent sequences: A046467 A046468 A046469 * A046471 A046472 A046473

Keyword

nonn

Author

Shyam Sunder Gupta, Feb 16 2002

Status

approved