A374291 -id:A374291 - cp's OEIS frontend

A374458 Squares of exponentially odd numbers (A268335).

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

Offset: 1

Amiram Eldar, Jul 09 2024

Numbers whose exponents in their prime factorization are all congruent to 2 (mod 4).

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A000290, A016825, A013662, A268335.

Similar sequences: A030140, A062503, A085986, A153158, A374291.

Select[Range[100], AllTrue[FactorInteger[#][[;;, 2]], OddQ] &]^2

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);

a(n) = A000290(A268335(n)) = A268335(n)^2.
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.

cp's OEIS Frontend

A374458 Squares of exponentially odd numbers (A268335).

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