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%I #21 Feb 13 2024 23:16:18
%S 8,25,77,125,133,209,301,325,425,469,473,725,737,817,925,1025,1141,
%T 1273,1325,1525,1625,1793,1825,2125,2225,2425,2525,2725,2825,2881,
%U 3097,3425,3625,3725,3925,4325,4525,4625,4825,4925,5125,5525,5725,5825,6025,6425
%N Integers k such that A231589(k) = floor(k*(k-1)/4) - k.
%C It appears that this sequence is the union of 3 sets.
%C First term is 8, and is the only even known value.
%C Then we get terms that are equal to 25 * b with b a squarefree product of primes congruent to 1 modulo 4 (A002144), that is, terms of A231754.
%C And we get the following terms 77, 133, 209, 301, 469, 473, 737, 817, 1141, 1273, 1793, 2881, 3097, 7009, 10921. These numbers are the products of 2 distinct primes from this list: 7, 11, 19, 43, 67, 163 (a subsequence of A003173).
%H Hugo Pfoertner, <a href="/A231791/b231791.txt">Table of n, a(n) for n = 1..10000</a>
%H John P. Robertson, <a href="https://web.archive.org/web/20180831181644/http://www.jpr2718.org/shir2.pdf">Shirali’s Questions About Sums of Residues of Squares</a>
%H S. A. Shirali, <a href="http://www.jstor.org/stable/2690862">A family portrait of primes-a case study in discrimination</a>, Math. Mag. Vol. 70, No. 4 (Oct., 1997), pp. 263-272.
%o (PARI) isok(n) = A231589(n) == n*(n-1)/4 - n;
%Y Cf. A231589.
%K nonn
%O 1,1
%A _Michel Marcus_, Nov 13 2013
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