A046340 Odd composite numbers with an odd number of prime factors (counted with multiplicity).

27, 45, 63, 75, 99, 105, 117, 125, 147, 153, 165, 171, 175, 195, 207, 231, 243, 245, 255, 261, 273, 275, 279, 285, 325, 333, 343, 345, 357, 363, 369, 385, 387, 399, 405, 423, 425, 429, 435, 455, 465, 475, 477, 483, 507, 531, 539, 549, 555, 561, 567, 575

Offset

1,1

Links

John Cerkan, Table of n, a(n) for n = 1..10000

Mathematica

Select[Range[3, 699, 2], OddQ[Total[Transpose[FactorInteger[#]][[2]]]] && !PrimeQ[#]&] (* Harvey P. Dale, Dec 09 2010 *)
Select[Range[3, 699, 2], CompositeQ[#]&&OddQ[PrimeOmega[#]]&] (* Harvey P. Dale, Jun 18 2024 *)

Prog

(Python)
from math import isqrt, prod
from sympy import primerange, integer_nthroot, primepi
from oeis_sequences.OEISsequences import bisection
def A046340(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+1+primepi(x)+sum(sum(primepi(x//prod(c[1] for c in a))-a[-1][0] for a in g(x, 0, 1, 1, m)) for m in range(2, x.bit_length()+1, 2))+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, n) # Chai Wah Wu, Dec 19 2025

Crossrefs

Cf. A046339, A046341.

Sequence in context: A259504 A307373 A121614 * A046316 A046373 A228057

Adjacent sequences: A046337 A046338 A046339 * A046341 A046342 A046343

Keyword

nonn

Author

Patrick De Geest, Jun 15 1998

Extensions

Name (description) modified by Harvey P. Dale, Dec 09 2010

Status

approved