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I corrected the above comment by adding the exponent (4b+1) to p, because otherwise it would miss cases terms like a(614) = 3125 = 5^5, a(1140) = 6250 = 2 * 5^5, a(4421) = 28125 = 5^5 * 3^2, occurring in this sequence as term a(4421)etc. - Antti Karttunen, May 25 2022
These numbers are exactly the numbers of the form 2^a * p ^(4b+1) * m^2 where p is a prime number congruent to 1 modulo 4, a is a nonnegative integer, and m is a positive integer coprime to p. In particular, they are also sums of two squares: the sequence has the first 12 terms in common with A132777.
Note: The I corrected the above does not cover comment by adding the exponent (4b+1) to p, because otherwise it would miss cases like 28125 = 5^5 * 3^2, occurring in this sequence as term a(4421). - Antti Karttunen, May 24 25 2022
Note: The above does not cover cases like 28125 = 5^5 * 3^2, occurring in this sequence as term a(4421). - Antti Karttunen, May 24 2022
Cf. A353812 (characteristic function).
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