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%I A367803 #10 Feb 26 2024 01:25:51
%S A367803 1,64,729,1024,4096,15625,46656,59049,117649,262144,531441,746496,
%T A367803 1000000,1048576,1771561,2985984,3779136,4826809,7529536,9765625,
%U A367803 11390625,16000000,16777216,24137569,34012224,47045881,60466176,64000000,85766121,113379904,120472576,148035889
%N A367803 Exponentially evil squares.
%C A367803 Numbers whose prime factorization contains only exponents that are even evil numbers (A125592).
%C A367803 Also, squares of exponentially evil numbers (A262675).
%C A367803 Also, numbers with an equal number of exponentially odious and exponentially evil divisors, i.e., numbers k such that A366901(k) = A366902(k). - _Amiram Eldar_, Feb 26 2024
%H A367803 Amiram Eldar, <a href="/A367803/b367803.txt">Table of n, a(n) for n = 1..10000</a>
%H A367803 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 A367803 a(n) = A262675(n)^2.
%F A367803 Sum_{n>=1} 1/a(n) = Product_{p prime} (1 + Sum_{k>=1} 1/p^A125592(k)) = Product_{p prime} f(1/p) = 1.01833932269003592136..., where f(x) = (2/(1-x^2) + Product_{k>=0} (1 - x^(2^k)) + Product_{k>=0} (1 - (-x)^(2^k)))/4.
%t A367803 evilQ[n_] := EvenQ[DigitCount[n, 2, 1]]; Select[Range[10^4]^2, #== 1 || AllTrue[FactorInteger[#][[;;, 2]], evilQ] &]
%o A367803 (PARI) isexpevil(n) = {my(f = factor(n)); for (i = 1, #f~, if(hammingweight(f[i, 2])%2, return (0))); 1;}
%o A367803 is(n) = issquare(n) && isexpevil(n);
%Y A367803 Intersection of A000290 and A262675.
%Y A367803 Cf. A366901, A366902, A367801, A367802, A367804.
%Y A367803 Cf. A001969, A125592.
%K A367803 nonn,easy,base
%O A367803 1,2
%A A367803 _Amiram Eldar_, Dec 01 2023

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