%I #8 Feb 06 2024 08:14:34

%S 2,3,4,5,6,7,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,25,26,28,29,

%T 30,31,33,34,35,36,37,38,39,41,42,43,44,45,46,47,48,49,50,51,52,53,55,

%U 57,58,59,60,61,62,63,65,66,67,68,69,70,71,73,74,75,76,77

%N Numbers whose maximal exponent in their prime factorization is a power of 2.

%C First differs from its subsequence A138302 \ {1} at n = 378: a(378) = 432 = 2^4 * 3^3 is not a term of A138302.

%C First differs from A096432, A220218 \ {1}, A335275 \ {1} and A337052 \ {1} at n = 56, and from A270428 \ {1} at n = 113.

%C Numbers k such that A051903(k) is a power of 2.

%C The asymptotic density of this sequence is 1/zeta(3) + Sum_{k>=2} (1/zeta(2^k+1) - 1/zeta(2^k)) = 0.87442038669659566330... .

%H Amiram Eldar, <a href="/A369938/b369938.txt">Table of n, a(n) for n = 1..10000</a>

%t pow2Q[n_] := n == 2^IntegerExponent[n, 2];

%t Select[Range[2, 100], pow2Q[Max[FactorInteger[#][[;; , 2]]]] &]

%o (PARI) ispow2(n) = n >> valuation(n, 2) == 1;

%o is(n) = n > 1 && ispow2(vecmax(factor(n)[, 2]));

%Y Cf. A000079, A002117, A051903.

%Y Subsequences: A001146, A001248, A005117, A030514, A030635, A050376, A062503, A113849, A138302 \ {1}, A179645.

%Y Similar sequences: A368714, A369937, A369939.

%Y Cf. A096432, A220218, A270428, A335275, A337052.

%K nonn,easy

%O 1,1

%A _Amiram Eldar_, Feb 06 2024