cp's OEIS Frontend

A115167 Odd numbers k such that k-1 and k+1 have the same number of prime divisors with multiplicity.

%I A115167 #19 Jan 11 2024 13:26:17
%S A115167 5,19,29,43,51,55,67,69,77,89,115,151,171,173,187,189,197,233,237,243,
%T A115167 245,249,267,271,283,285,291,295,307,317,329,341,343,349,355,403,405,
%U A115167 411,427,429,435,437,461,489,491,507,569,571,593,597,603,605,653,665
%N A115167 Odd numbers k such that k-1 and k+1 have the same number of prime divisors with multiplicity.
%H A115167 Amiram Eldar, <a href="/A115167/b115167.txt">Table of n, a(n) for n = 1..10000</a>
%t A115167 s = {}; o1 = 0; Do[o2 = PrimeOmega[n]; If[o1 == o2, AppendTo[s, n-1]]; o1 = o2, {n, 2, 666, 2}]; s (* _Amiram Eldar_, Sep 23 2019 *)
%t A115167 Select[Mean/@SequencePosition[PrimeOmega[Range[700]],{x_,_,x_}],OddQ] (* _Harvey P. Dale_, Jan 11 2024 *)
%o A115167 (PARI) g(n) = forstep(x=3, n, 2, p1=bigomega(x-1); p2=bigomega(x+1); if(p1==p2, print1(x",")))
%o A115167 (Python)
%o A115167 from sympy import primeomega
%o A115167 def aupto(limit):
%o A115167   prv, nxt, alst = 1, 2, []
%o A115167   for n in range(3, limit+1, 2):
%o A115167     if prv == nxt: alst.append(n)
%o A115167     prv, nxt = nxt, primeomega(n+3)
%o A115167   return alst
%o A115167 print(aupto(665)) # _Michael S. Branicky_, May 19 2021
%Y A115167 Subsequence of A280382.
%K A115167 easy,nonn
%O A115167 1,1
%A A115167 _Cino Hilliard_, Mar 03 2006