This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A367802 #9 Apr 22 2025 05:21:42
%S A367802 1,4,9,16,25,36,49,81,100,121,144,169,196,225,256,289,324,361,400,441,
%T A367802 484,529,625,676,784,841,900,961,1089,1156,1225,1296,1369,1444,1521,
%U A367802 1681,1764,1849,1936,2025,2116,2209,2304,2401,2500,2601,2704,2809,3025,3249
%N A367802 Exponentially odious squares.
%C A367802 First differs from A354180 at n = 226.
%C A367802 Numbers whose prime factorization contains only exponents that are even odious numbers (A128309).
%C A367802 Also, squares of exponentially odious numbers (A270428).
%H A367802 Amiram Eldar, <a href="/A367802/b367802.txt">Table of n, a(n) for n = 1..10000</a>
%H A367802 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 A367802 a(n) = A270428(n)^2.
%F A367802 Sum_{n>=1} 1/a(n) = Product_{p prime} (1 + Sum_{k>=1} 1/p^A128309(k)) = Product_{p prime} f(1/p) = 1.62202332101829028287..., where f(x) = 1 + (2/(1-x^2) - Product_{k>=0} (1 - x^(2^k)) - Product_{k>=0} (1 - (-x)^(2^k)))/4.
%t A367802 odiousQ[n_] := OddQ[DigitCount[n, 2, 1]]; Select[Range[150]^2, AllTrue[FactorInteger[#][[;;, 2]], odiousQ] &]
%o A367802 (PARI) isexpodious(n) = {my(f = factor(n)); for (i = 1, #f~, if(!(hammingweight(f[i, 2])%2), return (0))); 1;}
%o A367802 is(n) = issquare(n) && isexpodious(n);
%Y A367802 Intersection of A000290 and A270428.
%Y A367802 Cf. A367801, A367803, A367804.
%Y A367802 Cf. A000069, A128309, A270428, A354180.
%K A367802 nonn,easy,base
%O A367802 1,2
%A A367802 _Amiram Eldar_, Dec 01 2023