A269929 Records for the numbers of Pythagorean triples to which an integer belongs.
0, 1, 2, 4, 5, 7, 8, 10, 14, 23, 32, 38, 41, 53, 68, 71, 95, 113, 122, 158, 159, 203, 206, 221, 284, 287, 338, 341, 365, 368, 473, 476, 479, 608, 611, 662, 665, 743, 854, 1016, 1097, 1421, 1430, 1826, 1835, 1988, 2231, 2369, 2564, 2636, 3050, 3293, 3314, 4265, 4274, 5480, 5966, 6695, 7109, 7667, 7910, 9125, 9134
Offset: 1
Keywords
Links
- A. Tripathi, On Pythagorean triples containing a fixed integer, Fib. Q., 46/47 (2008/2009), 331-340. See Theorem 11.
- Index entries related to Pythagorean Triples.
Programs
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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);} lista(nn) = {last = -1; for (n=1, nn, if ((new = nbpt(n)) > last, print1(new, ", "); last = new;););}
Extensions
More terms from Jinyuan Wang, Mar 15 2019