A259687 Let m = A062695(n); a(n) is value of d in decomposition of m defined in Comments.

1, 1, 1, 81, 5, 7, 1, 1, 13, 1, 11, 1, 185, 1, 1, 7, 1, 27, 1, 1, 9, 1, 9, 9, 11, 3, 15, 325, 1, 11, 17, 1, 1, 1, 1, 1, 5, 25, 33, 11, 7, 47, 801, 5, 193, 1, 1, 1, 19, 11, 13, 25, 21, 17, 635, 5, 37, 1, 1, 1, 1, 177, 23, 1, 1, 43, 9, 1, 5465, 27, 1, 2721, 1, 17

Offset

1,4

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..74.

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: A110727 A005068 A366458 * A065793 A214104 A175241

Adjacent sequences: A259684 A259685 A259686 * A259688 A259689 A259690

Keyword

nonn

Author

N. J. A. Sloane, Jul 04 2015

Extensions

More terms from Jinyuan Wang, Jan 01 2021

Status

approved