A345744 Numbers k such that k and k+1 are products of at least 5 primes.

728, 944, 1215, 1376, 1539, 1700, 2024, 2079, 2295, 2511, 2624, 2672, 3087, 3104, 3159, 3320, 3375, 3807, 3824, 3968, 4095, 4374, 4940, 5103, 5264, 5480, 5535, 5624, 5750, 5775, 5967, 5984, 6075, 6344, 6399, 6560, 6831, 6875, 6975, 6992, 7208, 7424, 7695, 7749, 7856

Offset: 1

Author

Tanya Khovanova, Jun 25 2021

Keywords

• nonn

Comments

Integers k such that k and k+1 are in A046304. - Michel Marcus, Jun 26 2021

Examples

			728 = 2^3*7*13 is a product of 5 primes, while 729 = 3^6 is a product of 6 primes. Thus, 728 is in this sequence.
		

Crossrefs

Cf. A001222, A046304.

Programs

Maple

q:= n-> andmap(x-> numtheory[bigomega](x)>4, [n, n+1]):
select(q, [$1..8000])[];  # Alois P. Heinz, Jun 26 2021

Mathematica

Select[Range[10000], Total[Transpose[FactorInteger[#]][[2]]] > 4 && Total[Transpose[FactorInteger[# + 1]][[2]]] > 4 &]

PARI

isok(k) = (bigomega(k) >= 5) && (bigomega(k+1) >= 5); \\ Michel Marcus, Jun 26 2021

Python

from sympy import factorint
def ok(n): return all(sum(factorint(n+k).values()) > 4 for k in [0, 1])
print(list(filter(ok, range(8000)))) # Michael S. Branicky, Jun 25 2021