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A369938 Numbers whose maximal exponent in their prime factorization is a power of 2.

%I A369938 #10 Nov 06 2024 11:11:15
%S A369938 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 A369938 30,31,33,34,35,36,37,38,39,41,42,43,44,45,46,47,48,49,50,51,52,53,55,
%U A369938 57,58,59,60,61,62,63,65,66,67,68,69,70,71,73,74,75,76,77
%N A369938 Numbers whose maximal exponent in their prime factorization is a power of 2.
%C A369938 First differs from its subsequence A138302 \ {1} at n = 378: a(378) = 432 = 2^4 * 3^3 is not a term of A138302.
%C A369938 First differs from A096432, A220218 \ {1}, A335275 \ {1} and A337052 \ {1} at n = 56, and from A270428 \ {1} at n = 113.
%C A369938 Numbers k such that A051903(k) is a power of 2.
%C A369938 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 A369938 Amiram Eldar, <a href="/A369938/b369938.txt">Table of n, a(n) for n = 1..10000</a>
%t A369938 pow2Q[n_] := n == 2^IntegerExponent[n, 2];
%t A369938 Select[Range[2, 100], pow2Q[Max[FactorInteger[#][[;; , 2]]]] &]
%t A369938 Select[Range[2,80],IntegerQ[Log2[Max[FactorInteger[#][[;;,2]]]]]&] (* _Harvey P. Dale_, Nov 06 2024 *)
%o A369938 (PARI) ispow2(n) = n >> valuation(n, 2) == 1;
%o A369938 is(n) = n > 1 && ispow2(vecmax(factor(n)[, 2]));
%Y A369938 Cf. A000079, A002117, A051903.
%Y A369938 Subsequences: A001146, A001248, A005117, A030514, A030635, A050376, A062503, A113849, A138302 \ {1}, A179645.
%Y A369938 Similar sequences: A368714, A369937, A369939.
%Y A369938 Cf. A096432, A220218, A270428, A335275, A337052.
%K A369938 nonn,easy
%O A369938 1,1
%A A369938 _Amiram Eldar_, Feb 06 2024