cp's OEIS Frontend

A369329 Numbers whose neighbors have a prime number as their greatest odd divisor.

%I A369329 #24 Jul 30 2025 15:08:05
%S A369329 4,6,11,12,13,18,21,23,25,27,30,39,42,45,47,57,60,72,75,81,87,93,95,
%T A369329 102,105,108,117,123,135,138,147,150,159,165,177,180,192,193,198,207,
%U A369329 213,225,228,240,270,273,282,297,303,312,315,327,333,345,348,357,383,385,387
%N A369329 Numbers whose neighbors have a prime number as their greatest odd divisor.
%C A369329 Does this sequence contain a finite or infinite number of squares, powers of 3, even numbers, ...?
%H A369329 Harvey P. Dale, <a href="/A369329/b369329.txt">Table of n, a(n) for n = 1..1000</a>
%p A369329 filter:= proc(n) local m;
%p A369329     andmap(m -> isprime(m/2^padic:-ordp(m,2)), [n-1,n+1])
%p A369329 end proc:
%p A369329 select(filter, [$1..1000]); # _Robert Israel_, Jan 24 2024
%t A369329 q[n_] := PrimeQ[n / 2^IntegerExponent[n, 2]]; Select[Range[400], And @@ q /@ {# - 1, # + 1} &] (* _Amiram Eldar_, Jan 20 2024 *)
%t A369329 Mean/@SequencePosition[Table[If[PrimeQ[Select[Divisors[n],OddQ][[-1]]],1,0],{n,400}],{1,_,1}] (* _Harvey P. Dale_, Jul 30 2025 *)
%o A369329 (Magma) [k: k in [2..400] | #Divisors(2*k-2)-#Divisors(k-1) eq 2 and #Divisors(2*k+2)-#Divisors(k+1) eq 2];
%Y A369329 Supersequence of A014574 and A276136.
%Y A369329 Cf. A038550, A273401, A275418.
%K A369329 nonn
%O A369329 1,1
%A A369329 _Juri-Stepan Gerasimov_, Jan 20 2024