

A269929


Records for the numbers of Pythagorean triples to which an integer belongs.


1



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
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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), 331340. 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 * A085370 A006693 A281641
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



