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

Author

Michel Marcus, Mar 08 2016

Keywords

• nonn

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.

Crossrefs

Cf. A046081, A269928.

Programs

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;););}

Formula

a(n) = A046081(A269928(n)).

Extensions

More terms from Jinyuan Wang, Mar 15 2019