A384372 Numbers m such that both m-1 and m+1 are the product of at least 4 not necessarily distinct primes.

55, 89, 127, 151, 161, 197, 199, 209, 233, 249, 251, 271, 295, 305, 307, 329, 341, 343, 349, 351, 377, 379, 391, 415, 449, 461, 463, 485, 487, 489, 491, 511, 521, 545, 551, 559, 569, 571, 593, 631, 649, 665, 685, 687, 689, 701, 703, 713, 727, 737, 739, 749, 751

Offset: 1

Author

Sinuhe Perea, May 27 2025

Keywords

• nonn

Comments

Numbers m such that bigomega(m-1) >= 4 and bigomega(m+1) >= 4.

Examples

			55 is in the sequence because 55-1 = 2*3^3 and 55+1 = 2^3*7 are both products of at least 4 primes.
71 is not in the sequence because 71-1 = 2*5*7.
		

Crossrefs

Cf. A001222, A176462.

Programs

Maple

q:= n-> andmap(x-> numtheory[bigomega](x)>3, [n-1, n+1]):
select(q, [$1..991])[];  # Alois P. Heinz, Jun 12 2025

PARI

isok(m) = (m>1) && (bigomega(m-1)>3) && (bigomega(m+1)>3); \\ Michel Marcus, Jun 12 2025

Python

from sympy import primeomega
def ok(n): return n>1 and primeomega(n-1)>3 and primeomega(n+1)>3
print(list(filter(ok, range(520))))