A355813 Number of solutions (p,q) to 1/s^2 + 1/t^2 = 1/p^2 + 1/q^2 where p,q < t = A355812(n).

1, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 3, 2, 2, 1, 2, 2, 2, 4, 1, 2, 4, 2, 2, 3, 2, 2, 2, 2, 2, 2, 4, 3, 2, 2, 4, 2, 1, 2, 2, 6, 2, 2, 4, 3, 2, 1, 2, 2, 2, 2, 2, 2, 2, 3, 4, 4, 2, 2, 1, 2, 6, 1, 2, 6, 4, 2, 4, 1, 2, 2, 8

Offset

1,2

Links

Jianing Song, Table of n, a(n) for n = 1..307

Example

A355812(1) = 35. 1/s^2 + 1/35^2 = 1/p^2 + 1/q^2 has one solution, (s,p,q) = (5,7,7), so a(1) = 35.
A355812(2) = 55. 1/s^2 + 1/55^2 = 1/p^2 + 1/q^2 has two solutions, (s,p,q) = (10,11,22) and (10,22,11), so a(2) = 55.
A355812(32) = 210. 1/s^2 + 1/210^2 = 1/p^2 + 1/q^2 has three solutions, (s,p,q) = (30,42,42), (95,114,133) and (95,133,114), so a(32) = 3.

Prog

(PARI) b(n) = my(v=[; ], r); for(p=1, n-1, for(q=1, n-1, r=1/(1/p^2+1/q^2-1/n^2); if(r==r\1 && issquare(r), v=concat(v, [p; q])))); v
list(lim) = my(v=[], num); for(n=1, lim, if((num=#b(n))>0, v=concat(v, num))); v

Crossrefs

Cf. A355812, A355814.

Sequence in context: A276337 A160385 A076881 * A136754 A276788 A282625

Adjacent sequences: A355810 A355811 A355812 * A355814 A355815 A355816

Keyword

nonn

Author

Jianing Song, Jul 18 2022

Status

approved