A376861 Numbers with a composite number of prime factors and a composite number of distinct prime factors.

210, 330, 390, 462, 510, 546, 570, 690, 714, 770, 798, 840, 858, 870, 910, 930, 966, 1110, 1122, 1155, 1190, 1218, 1230, 1254, 1260, 1290, 1302, 1320, 1326, 1330, 1365, 1410, 1430, 1482, 1518, 1554, 1560, 1590, 1610, 1722, 1770, 1785, 1794, 1806, 1830, 1848, 1870, 1890, 1914, 1938, 1974, 1980, 1995

Offset: 1

Author

Marc Morgenegg, Feb 05 2025

Keywords

• nonn

Examples

			840 is a term since 840 = 2 * 2 * 2 * 3 * 5 * 7 has 6 prime factors and 4 distinct prime factors, and both 6 and 4 are composite.
		

Crossrefs

Cf. A001221, A001222, A002808.

Programs

Mathematica

Select[Range[2000],CompositeQ[PrimeOmega[#]]&&CompositeQ[PrimeNu[#]]&] (* James C. McMahon, Feb 13 2025 *)

Python

from sympy import factorint, isprime
def ok(n):
    f = factorint(n)
    w, W = len(f), sum(e for e in f.values())
    return w > 3 and W > 3 and not isprime(w) and not isprime(W)
print([k for k in range(1, 2000) if ok(k)]) # Michael S. Branicky, Feb 07 2025

Formula

{k | A001221(k) in A002808 and A001222(k) in A002808}. - Michael S. Branicky, Feb 07 2025