A363122 - OEIS

%I #16 Oct 04 2023 06:49:05

%S 2,4,8,12,16,24,32,40,48,56,64,80,96,112,120,128,144,160,168,176,192,

%T 208,224,240,256,280,288,320,336,352,384,416,448,480,512,528,544,560,

%U 576,608,624,640,672,704,720,736,768,800,832,840,864,880,896,928,960,992

%N 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 Numbers k such that A006519(k) = A034699(k).

%C 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 Amiram Eldar, <a href="/A363122/b363122.txt">Table of n, a(n) for n = 1..10000</a>

%t q[n_] := Module[{e = IntegerExponent[n, 2]}, 2^e > Max[Power @@@ FactorInteger[n/2^e]]]; Select[Range[1000], q]

%o (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 (Python)

%o from itertools import count, islice

%o from sympy import factorint

%o def A363122_gen(startvalue=2): # generator of terms >= startvalue

%o     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_list = list(islice(A363122_gen(),20)) # _Chai Wah Wu_, May 17 2023

%Y Cf. A006519, A034699, A116882, A363123.

%Y Subsequence of A174973.

%K nonn,easy

%O 1,1

%A _Amiram Eldar_, May 16 2023