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

1,1

Links

Table of n, a(n) for n=1..53.

Formula

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Cf. A001221, A001222, A002808.

Sequence in context: A127424 A074159 A033993 * A350373 A046386 A379762

Adjacent sequences: A376858 A376859 A376860 * A376862 A376863 A376864

Keyword

nonn,new

Author

Marc Morgenegg, Feb 05 2025

Status

approved