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%I #7 Jul 10 2024 02:58:24
%S 1,4,9,25,36,49,64,100,121,169,196,225,289,361,441,484,529,576,676,
%T 729,841,900,961,1024,1089,1156,1225,1369,1444,1521,1600,1681,1764,
%U 1849,2116,2209,2601,2809,2916,3025,3136,3249,3364,3481,3721,3844,4225,4356,4489
%N Squares of exponentially odd numbers (A268335).
%C Numbers whose exponents in their prime factorization are all congruent to 2 (mod 4).
%H Amiram Eldar, <a href="/A374458/b374458.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A000290(A268335(n)) = A268335(n)^2.
%F Sum_{n>=1} 1/a(n) = zeta(4) * Product_{p prime} (1 + 1/p^2 - 1/p^4) = 1.54211628314015874165... .
%F Sum_{n>=1} 1/a(n)^s = zeta(4*s) * Product_{p prime} (1 + 1/p^(2*s) - 1/p^(4*s)), for s > 1/2.
%t Select[Range[100], AllTrue[FactorInteger[#][[;;, 2]], OddQ] &]^2
%o (PARI) is(k) = issquare(k) && if(k == 1, 1, my(e = factor(k)[, 2]); for(i = 1, #e, if(e[i] % 4 != 2, return(0))); 1);
%Y Cf. A000290, A016825, A013662, A268335.
%Y Similar sequences: A030140, A062503, A085986, A153158, A374291.
%K nonn,easy
%O 1,2
%A _Amiram Eldar_, Jul 09 2024
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