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A367804 Numbers that are both exponentially odd (A268335) and exponentially evil (A262675).

%I A367804 #6 Dec 01 2023 15:54:35
%S A367804 1,8,27,32,125,216,243,343,512,864,1000,1331,1944,2197,2744,3125,3375,
%T A367804 4000,4913,6859,7776,9261,10648,10976,12167,13824,16807,17576,19683,
%U A367804 24389,25000,27000,29791,30375,32768,35937,39304,42592,42875,50653,54872,59319,64000
%N A367804 Numbers that are both exponentially odd (A268335) and exponentially evil (A262675).
%C A367804 Numbers whose prime factorization contains only exponents that are odd evil numbers (A129771).
%H A367804 Amiram Eldar, <a href="/A367804/b367804.txt">Table of n, a(n) for n = 1..10000</a>
%H A367804 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.
%F A367804 Sum_{n>=1} 1/a(n) = Product_{p prime} (1 + Sum_{k>=1} 1/p^A129771(k)) = Product_{p prime} f(1/p) = 1.22183814098622400889..., where f(x) = 1 + (2*x/(1-x^2) + Product_{k>=0} (1 - x^(2^k)) - Product_{k>=0} (1 - (-x)^(2^k)))/4.
%t A367804 q[n_] := OddQ[n] && EvenQ[DigitCount[n, 2, 1]]; Select[Range[150], #== 1 || AllTrue[FactorInteger[#][[;;, 2]], q] &]
%o A367804 (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 A367804 Intersection of A262675 and A268335.
%Y A367804 Cf. A367801, A367802, A367803.
%Y A367804 Cf. A129771.
%K A367804 nonn,easy,base
%O A367804 1,2
%A A367804 _Amiram Eldar_, Dec 01 2023