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%I #26 Jan 31 2023 04:27:09
%S 3,9,16,22,28,35,40,48,53,60,66,72,78,85,91,98,103,110,117,122,129,
%T 135,141,148,154,160,167,173,179,185,192,197,205,210,217,223,229,236,
%U 242,248,255,260,267,274,279,286,292,299,304,311,318,323,330,336,343,349,355,361,367
%N a(n) is the number of circles of positive integer area with radii less than n and greater than n - 1.
%C Conjecture: k >= 2, each triple Tr(k) = {a(k), a(k+1), a(k+2)} gives the sides of an integer-sided triangle, and {(a(k+2) - a(k)), (a(k+2) - a(k+1)), (a(k+1) - a(k))} is a degenerate integer-sided triangle.
%F a(n) = #{floor(sqrt(k/Pi)) < n: n > 0, k > 0}.
%F a(n) = A066643(n)-A066643(n-1). - _R. J. Mathar_, Jan 25 2023
%o (PARI) ap(n) = {my(x = 0, y = 1, ia = 1); while(y, if(n > sqrt(ia / Pi), x++; ia++, y = 0)); return(x)}
%o a(n) = {my(x = 0, y = 1, ia = 1); while(y, if(n > sqrt(ia / Pi), x++; ia++, y = 0)); return(x - ap(n-1))}
%o for(i = 1, 70, print1(a(i), ", "))
%Y Cf. A066643 (partial sums).
%K nonn
%O 1,1
%A _Torlach Rush_, Oct 06 2020