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A152492 a(n) = number of integers of the form (n*k)^2/(k^2 - n^2).

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%I A152492 #29 Oct 28 2022 14:22:49
%S A152492 0,0,1,1,0,2,0,1,1,1,0,8,0,0,4,1,0,2,0,4,3,0,0,9,0,0,1,2,0,7,0,1,2,0,
%T A152492 1,8,0,0,1,4,0,5,0,1,5,0,0,9,0,1,1,1,0,2,1,4,1,0,0,23,0,0,3,1,1,4,0,1,
%U A152492 1,2,0,10,0,0,4,1,0,4,0,4,1,0,0,17,0,0,1,1,0,8
%N A152492 a(n) = number of integers of the form (n*k)^2/(k^2 - n^2).
%C A152492 k needs to be checked only up through n^2+1 since beyond this n^2 < (n*k)^2/(k^2 - n^2) < n^2 + 1 and thus can't be an integer. - _Micah Manary_, Aug 27 2022
%H A152492 Micah Manary, <a href="/A152492/b152492.txt">Table of n, a(n) for n = 1..1000</a>
%o A152492 (PARI) a(n) = sum(k=1, n^2+1, if (k!=n, denominator((n*k)^2/(k^2 - n^2))==1)); \\ _Michel Marcus_, Oct 28 2022
%Y A152492 Cf. A071086, A146567, A146566, A146564.
%K A152492 easy,nonn
%O A152492 1,6
%A A152492 _Ctibor O. Zizka_, Dec 06 2008
%E A152492 More terms from _Micah Manary_, Aug 07 2022