A259685 Let m = A062695(n); a(n) is value of b in decomposition of m defined in Comments.

2, 4, 2, 56, 1, 2, 1, 1, 6, 1, 4, 4, 104, 2, 4, 1, 12, 4, 1, 8, 2, 6, 1, 2, 5, 1, 2, 204, 1, 2, 4, 1, 4, 3, 2, 1, 1, 12, 20, 3, 20, 4, 40, 3, 132, 6, 3, 2, 6, 2, 82, 17, 11, 4, 333, 14, 12, 6, 5, 2, 1, 52, 1, 12, 2, 29, 1, 1, 1972, 7, 24, 1504, 20, 360, 10, 2952

Offset

1,1

Comments

Let m = A062695(n). Write m*y^2 = x^3 - x as m*square = A*B*(A-B)*(A+B) where A and B are the numerator and denominator of x. Then A, B, A-B, A+B have the form s*a^2, t*b^2, u*c^2, v*d^2 for some decomposition of m as s*t*u*v and some natural numbers a,b,c,d. These eight numbers are given in A259680-A259687.

Links

Table of n, a(n) for n=1..76.

G. Kramarz, All congruent numbers less than 2000, Math. Annalen, 273 (1986), 337-340.

G. Kramarz, All congruent numbers less than 2000, Math. Annalen, 273 (1986), 337-340. [Annotated, corrected, scanned copy]

Crossrefs

Cf. A003273, A006991, A062695, A259680-A259687.

Sequence in context: A361077 A263931 A375902 * A301460 A130172 A303320

Adjacent sequences: A259682 A259683 A259684 * A259686 A259687 A259688

Keyword

nonn

Author

N. J. A. Sloane, Jul 04 2015

Extensions

More terms from Jinyuan Wang, Jan 01 2021

Status

approved