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

1,1

Comments

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

Links

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

Example

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.

Maple

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

Prog

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

Crossrefs

Cf. A001222, A176462.

Sequence in context: A366848 A320507 A039533 * A157484 A230125 A027865

Adjacent sequences: A384369 A384370 A384371 * A384373 A384374 A384375

Keyword

nonn

Author

Sinuhe Perea, May 27 2025

Status

approved