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A363122 Numbers k such that the highest power of 2 dividing k is larger than the highest power of p dividing k for any odd prime p.

%I A363122 #16 Oct 04 2023 06:49:05
%S A363122 2,4,8,12,16,24,32,40,48,56,64,80,96,112,120,128,144,160,168,176,192,
%T A363122 208,224,240,256,280,288,320,336,352,384,416,448,480,512,528,544,560,
%U A363122 576,608,624,640,672,704,720,736,768,800,832,840,864,880,896,928,960,992
%N A363122 Numbers k such that the highest power of 2 dividing k is larger than the highest power of p dividing k for any odd prime p.
%C A363122 Numbers k such that A006519(k) = A034699(k).
%C A363122 If k is a term of this sequence then k*2^m is a term for any m >= 0. The primitive terms are in A363123.
%H A363122 Amiram Eldar, <a href="/A363122/b363122.txt">Table of n, a(n) for n = 1..10000</a>
%t A363122 q[n_] := Module[{e = IntegerExponent[n, 2]}, 2^e > Max[Power @@@ FactorInteger[n/2^e]]]; Select[Range[1000], q]
%o A363122 (PARI) is(n) = {my(e = valuation(n, 2), m = n>>e); if(m == 1, n>1, f = factor(m); 2^e > vecmax(vector(#f~, i, f[i, 1]^f[i, 2]))); }
%o A363122 (Python)
%o A363122 from itertools import count, islice
%o A363122 from sympy import factorint
%o A363122 def A363122_gen(startvalue=2): # generator of terms >= startvalue
%o A363122     return filter(lambda n:n&-n>max((p**e for p, e in factorint(n>>(~n&n-1).bit_length()).items()),default=0),count(max(startvalue,2)))
%o A363122 A363122_list = list(islice(A363122_gen(),20)) # _Chai Wah Wu_, May 17 2023
%Y A363122 Cf. A006519, A034699, A116882, A363123.
%Y A363122 Subsequence of A174973.
%K A363122 nonn,easy
%O A363122 1,1
%A A363122 _Amiram Eldar_, May 16 2023