A300476 Numbers the square of which can be written as a sum of four nonzero bi-quadratics.

2, 7, 8, 17, 18, 23, 28, 32, 50, 63, 68, 72, 82, 92, 97, 98, 103, 112, 122, 128, 137, 153, 162, 175, 177, 178, 200, 207, 242, 252, 257, 272, 288, 303, 328, 337, 338, 343, 367, 368, 369, 388, 392, 393, 412, 417, 425, 433, 448, 450, 478, 487, 488, 503, 512, 548, 567, 575

Offset

1,1

Comments

Numbers w which can be expressed as w^2 = x^4 +y^4 +z^4 +t^4 with x,y,z,t >0. Values that have more than one representation (w=63, 153, 207, 252,...) are listed only once.

Links

Table of n, a(n) for n=1..58.

A. Alvarado, J.-J. Delorme, On the diophantine equation x^4+y^4+z^4+t^4=w^2, J. Int. Seq. 17 (2014) # 14.11.5.

Example

2^2 = 1^4 +1^4 +1^4 +1^4. 7^2 = 1^4 +2^4 +2^4 +2^4. 8^2 = 2^4 +2^4 +2^4 +2^4. 17^2 = 1^2 +2^4 +2^4 +4^4. 18^2=3^4 +3^4 +3^4 +3^4. 23^2 = 1^2 +2^4 +4^4 +4^4.

Crossrefs

Sequence in context: A341706 A032689 A331489 * A213037 A287343 A101518

Adjacent sequences: A300473 A300474 A300475 * A300477 A300478 A300479

Keyword

nonn

Author

R. J. Mathar, Mar 06 2018

Status

approved