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A367801 Numbers that are both exponentially odd (A268335) and exponentially odious (A270428).

%I A367801 #9 Dec 01 2023 15:53:57
%S A367801 1,2,3,5,6,7,10,11,13,14,15,17,19,21,22,23,26,29,30,31,33,34,35,37,38,
%T A367801 39,41,42,43,46,47,51,53,55,57,58,59,61,62,65,66,67,69,70,71,73,74,77,
%U A367801 78,79,82,83,85,86,87,89,91,93,94,95,97,101,102,103,105,106
%N A367801 Numbers that are both exponentially odd (A268335) and exponentially odious (A270428).
%C A367801 First differs from its subsequence A005117 at n = 79: a(79) = 128 is not a squarefree number.
%C A367801 First differs from A077377 at n = 63, and from A348506 at n = 68.
%C A367801 Numbers whose prime factorization contains only exponents that are odd odious numbers (A092246).
%C A367801 The asymptotic density of this sequence is Product_{p prime} f(1/p) = 0.61156148494581943994..., where f(x) = (1-x) * (1 + x/(2*(1-x^2)) + (Product_{k>=0} (1-(-x)^(2^k)) - Product_{k>=0} (1-x^(2^k))))/2.
%H A367801 Amiram Eldar, <a href="/A367801/b367801.txt">Table of n, a(n) for n = 1..12232</a> (terms below 20000)
%H A367801 Vladimir Shevelev, <a href="http://dx.doi.org/10.4064/aa8395-5-2016">S-exponential numbers</a>, Acta Arithmetica, Vol. 175 (2016), pp. 385-395.
%t A367801 odQ[n_] := OddQ[n] && OddQ[DigitCount[n, 2, 1]]; Select[Range[150], AllTrue[FactorInteger[#][[;;, 2]], odQ] &]
%o A367801 (PARI) is(n) = {my(f = factor(n)); for (i = 1, #f~, if(!(f[i, 2]%2 && hammingweight(f[i, 2])%2), return (0))); 1;}
%Y A367801 Intersection of A268335 and A270428.
%Y A367801 Cf. A367802, A367803, A367804.
%Y A367801 Subsequences: A005117, A092759.
%Y A367801 Cf. A092246.
%Y A367801 Cf. A077377, A348506.
%K A367801 nonn,easy,base
%O A367801 1,2
%A A367801 _Amiram Eldar_, Dec 01 2023