A346207 Numbers k such that k and k+1 are products of at least 6 primes.

1215, 3968, 5103, 5264, 6560, 7424, 7695, 8991, 9375, 9800, 11024, 11583, 11744, 12375, 12879, 13040, 14175, 14336, 14624, 15624, 16064, 16280, 16767, 16928, 17199, 17576, 18224, 21375, 21735, 22112, 22599, 22815, 23408, 24255, 24543, 24704, 24975, 25839, 26000, 26487, 27135

Offset: 1

Author

Tanya Khovanova, Jul 10 2021

Keywords

• nonn

Comments

Integers k such that k and k+1 are in A046305.

Examples

			1215 = 3^5*5 is a product of 6 primes. The next integer, 1216 = 2^6*19, is a product of 7 primes. Thus, 1215 is in this sequence.
		

Crossrefs

Cf. A046305, A345744.

Programs

Maple

q:= n-> andmap(x-> numtheory[bigomega](x)>5, [n, n+1]):
select(q, [$1..30000])[];  # Alois P. Heinz, Jul 10 2021

Mathematica

Select[Range[100000], Total[Transpose[FactorInteger[#]][[2]]] >= 6 && Total[Transpose[FactorInteger[# + 1]][[2]]] >= 6 &]

PARI

isA346207(k) = (bigomega(k) >= 6) && (bigomega(k+1) >= 6) \\ Jianing Song, Jul 10 2021

Python

from sympy import factorint
def prod6(n): return sum(factorint(n).values()) >= 6
def aupto(lim): return [k for k in range(lim+1) if prod6(k) and prod6(k+1)]
print(aupto(27135)) # Michael S. Branicky, Jul 10 2021