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

%I A280382 #18 May 24 2021 07:57:58
%S A280382 4,5,6,12,18,19,29,30,34,42,43,50,51,55,56,60,67,69,72,77,86,89,92,94,
%T A280382 102,108,115,120,122,138,142,144,150,151,160,171,173,180,184,186,187,
%U A280382 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
%N A280382 Numbers k such that k-1 has the same number of prime factors counted with multiplicity as k+1.
%H A280382 Rick L. Shepherd, <a href="/A280382/b280382.txt">Table of n, a(n) for n = 1..10000</a>
%e A280382 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.
%t A280382 Select[Range[2, 300], Equal @@ PrimeOmega[# + {-1, 1}] &] (* _Amiram Eldar_, May 20 2021 *)
%o A280382 (PARI) IsInA280382(n) = n > 1 && bigomega(n-1) == bigomega(n+1)
%o A280382 (Python)
%o A280382 from sympy import primeomega
%o A280382 def aupto(limit):
%o A280382   prv, cur, nxt, alst = 1, 1, 2, []
%o A280382   for n in range(3, limit+1):
%o A280382     if prv == nxt: alst.append(n)
%o A280382     prv, cur, nxt = cur, nxt, primeomega(n+2)
%o A280382   return alst
%o A280382 print(aupto(282)) # _Michael S. Branicky_, May 20 2021
%Y A280382 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).
%Y A280382 Cf. A115167 (subsequence of odd terms).
%K A280382 nonn
%O A280382 1,1
%A A280382 _Rick L. Shepherd_, Jan 01 2017