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

1,3

Links

Table of n, a(n) for n=1..63.

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.

Formula

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

Prog

(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; ); ); }

Crossrefs

Cf. A046081, A269928.

Sequence in context: A050054 A018371 A127964 * A364238 A085370 A006693

Adjacent sequences: A269926 A269927 A269928 * A269930 A269931 A269932

Keyword

nonn

Author

Michel Marcus, Mar 08 2016

Extensions

More terms from Jinyuan Wang, Mar 15 2019

Status

approved