A280382 Numbers k such that k-1 has the same number of prime factors counted with multiplicity as k+1.

4, 5, 6, 12, 18, 19, 29, 30, 34, 42, 43, 50, 51, 55, 56, 60, 67, 69, 72, 77, 86, 89, 92, 94, 102, 108, 115, 120, 122, 138, 142, 144, 150, 151, 160, 171, 173, 180, 184, 186, 187, 189, 192, 197, 198, 202, 204, 214, 216, 218, 220, 228, 233, 236, 237, 240, 243, 245, 248, 249, 266, 267, 270, 271, 274, 282

Offset: 1

Author

Rick L. Shepherd, Jan 01 2017

Keywords

• nonn

Examples

			Unlike for A088070, 5 is a term here because 4 = 2^2 and 6 = 2*3 each have two prime factors when counted with multiplicity. Similarly, 3 is not a term of this sequence (but is in A088070) because 2 and 4 have different numbers of prime factors as counted by A001222.
		

Links

• Rick L. Shepherd, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001222, A088070 (similar but prime factors counted without multiplicity), A280383 (prime factor count is same both ways), A280469 (subsequence of current with k-1 and k+1 squarefree also), A045920 (similar but for k and k+1).

Cf. A115167 (subsequence of odd terms).

Programs

Mathematica

Select[Range[2, 300], Equal @@ PrimeOmega[# + {-1, 1}] &] (* Amiram Eldar, May 20 2021 *)

PARI

IsInA280382(n) = n > 1 && bigomega(n-1) == bigomega(n+1)

Python

from sympy import primeomega
def aupto(limit):
  prv, cur, nxt, alst = 1, 1, 2, []
  for n in range(3, limit+1):
    if prv == nxt: alst.append(n)
    prv, cur, nxt = cur, nxt, primeomega(n+2)
  return alst
print(aupto(282)) # Michael S. Branicky, May 20 2021