

A280382


Numbers k such that k1 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
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OFFSET

1,1


LINKS

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


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(n1) == 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 k1 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
Adjacent sequences: A280379 A280380 A280381 * A280383 A280384 A280385


KEYWORD

nonn


AUTHOR

Rick L. Shepherd, Jan 01 2017


STATUS

approved



