A259681 Let m = A062695(n); a(n) is value of t in decomposition of m defined in Comments.

2, 1, 1, 1, 1, 5, 2, 7, 2, 2, 3, 2, 1, 1, 3, 13, 1, 19, 5, 1, 7, 2, 1, 10, 1, 31, 26, 1, 15, 5, 2, 6, 1, 2, 1, 3, 47, 2, 1, 1, 3, 43, 1, 3, 1, 2, 7, 10, 5, 15, 1, 1, 1, 59, 1, 1, 1, 1, 1, 2, 13, 1, 191, 2, 1, 1, 31, 15, 2, 5, 1, 1, 1, 1, 2, 1, 5, 13, 2, 7, 19

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..81.

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: A356299 A327858 A307372 * A146314 A202480 A124341

Adjacent sequences: A259678 A259679 A259680 * A259682 A259683 A259684

Keyword

nonn

Author

N. J. A. Sloane, Jul 04 2015

Extensions

More terms from Jinyuan Wang, Jan 01 2021

Status

approved