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A280382
Numbers k such that k-1 has the same number of prime factors counted with multiplicity as k+1.
6
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
1,1
LINKS
EXAMPLE
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.
MATHEMATICA
Select[Range[2, 300], Equal @@ PrimeOmega[# + {-1, 1}] &] (* Amiram Eldar, May 20 2021 *)
PROG
(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
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).
Sequence in context: A047429 A301289 A310571 * A055033 A089119 A063833
KEYWORD
nonn
AUTHOR
Rick L. Shepherd, Jan 01 2017
STATUS
approved