A269928 Integers n that belong to more Pythagorean triples than preceding integers.

1, 3, 5, 12, 15, 24, 40, 48, 60, 120, 240, 360, 420, 720, 840, 1560, 1680, 2520, 3360, 5040, 8400, 9240, 10920, 15120, 18480, 21840, 27720, 32760, 36960, 43680, 55440, 65520, 109200, 110880, 120120, 166320, 196560, 221760, 240240, 360360, 480480, 720720, 1113840

Offset: 1

Author

Michel Marcus, Mar 08 2016

Keywords

• nonn

Comments

Called optimal P-numbers in Tripathi link.

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, A269929.

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(n, ", "); last = new;););}