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A259685 Let m = A062695(n); a(n) is value of b in decomposition of m defined in Comments. 0
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 (list; graph; refs; listen; history; text; internal format)
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: A210457 A006496 A263931 * 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

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Last modified June 19 20:27 EDT 2021. Contains 345145 sequences. (Running on oeis4.)