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%I #10 Mar 16 2019 18:49:07
%S 0,1,2,4,5,7,8,10,14,23,32,38,41,53,68,71,95,113,122,158,159,203,206,
%T 221,284,287,338,341,365,368,473,476,479,608,611,662,665,743,854,1016,
%U 1097,1421,1430,1826,1835,1988,2231,2369,2564,2636,3050,3293,3314,4265,4274,5480,5966,6695,7109,7667,7910,9125,9134
%N Records for the numbers of Pythagorean triples to which an integer belongs.
%H A. Tripathi, <a href="http://www.fq.math.ca/Papers1/46_47-4/Tripathi.pdf">On Pythagorean triples containing a fixed integer</a>, Fib. Q., 46/47 (2008/2009), 331-340. See Theorem 11.
%H <a href="/index/Ps#PyTrip">Index entries related to Pythagorean Triples.</a>
%F a(n) = A046081(A269928(n)).
%o (PARI) nbpt(n) = {oddn = n/(2^valuation(n, 2)); f = factor(oddn); for (k=1, #f~, if ((f[k,1] % 4) != 1, f[k,2] = 0);); n1 = factorback(f); if (n % 2, (numdiv(n^2)+numdiv(n1^2))/2 -1, (numdiv((n/2)^2)+numdiv(n1^2))/2 -1);}
%o lista(nn) = {last = -1; for (n=1, nn, if ((new = nbpt(n)) > last, print1(new, ", "); last = new;););}
%Y Cf. A046081, A269928.
%K nonn
%O 1,3
%A _Michel Marcus_, Mar 08 2016
%E More terms from _Jinyuan Wang_, Mar 15 2019
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