A259680 Let m = A062695(n); a(n) is value of s in decomposition of m defined in Comments.

1, 1, 1, 137, 6, 29, 1, 1, 97, 5, 73, 1, 1, 1, 1, 1, 1, 17, 6, 1, 53, 1, 5, 41, 6, 2, 1, 1, 1, 101, 257, 7, 17, 1, 1, 7, 2, 337, 689, 7, 1, 1, 761, 37, 793, 1, 1, 1, 181, 61, 1, 21, 5, 1, 151, 1, 1, 1, 7, 1, 1, 1145, 2, 1, 11, 7, 2, 1, 593, 1, 1, 1217, 1, 1, 641

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..75.

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: A001330 A091510 A134885 * A082726 A189998 A138358

Adjacent sequences: A259677 A259678 A259679 * A259681 A259682 A259683

Keyword

nonn

Author

N. J. A. Sloane, Jul 04 2015

Extensions

More terms from Jinyuan Wang, Jan 01 2021

Status

approved