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A374458
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Squares of exponentially odd numbers (A268335).
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2
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1, 4, 9, 25, 36, 49, 64, 100, 121, 169, 196, 225, 289, 361, 441, 484, 529, 576, 676, 729, 841, 900, 961, 1024, 1089, 1156, 1225, 1369, 1444, 1521, 1600, 1681, 1764, 1849, 2116, 2209, 2601, 2809, 2916, 3025, 3136, 3249, 3364, 3481, 3721, 3844, 4225, 4356, 4489
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OFFSET
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1,2
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COMMENTS
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Numbers whose exponents in their prime factorization are all congruent to 2 (mod 4).
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LINKS
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FORMULA
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Sum_{n>=1} 1/a(n) = zeta(4) * Product_{p prime} (1 + 1/p^2 - 1/p^4) = 1.54211628314015874165... .
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.
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MATHEMATICA
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Select[Range[100], AllTrue[FactorInteger[#][[;; , 2]], OddQ] &]^2
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PROG
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(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);
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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