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1, 1, 1, 81, 5, 7, 1, 1, 13, 1, 11, 1, 185, 1, 1, 7, 1, 27, 1, 1, 9, 1, 99, 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

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.

G. Kramarz, <a href="/A003273/a003273.pdf"> All congruent numbers less than 2000</a>, Math. Annalen, 273 (1986), 337-340. [Annotated, corrected, scanned copy]

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More terms from Jinyuan Wang, Jan 01 2021

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qd

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

G. Kramarz, <a href="http://dx.doi.org/10.1007/BF01451411">All congruent numbers less than 2000</a>, Math. Annalen, 273 (1986), 337-340.

G. Kramarz, <a href="/A003273/a003273.pdf"> All congruent numbers less than 2000</a>, Math. Annalen, 273 (1986), 337-340. [Annotated, corrected, scanned copy]

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

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allocated for N. J. A. Sloane

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1, 1, 1, 81, 5, 7, 1, 1, 13, 1, 11, 1, 185, 1, 1, 7, 1, 27, 1, 1, 9, 1, 99, 11, 3, 15, 325, 1, 11, 17

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N. J. A. Sloane, Jul 04 2015

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