A124969 Numbers which can be expressed as an ordered sum of 3 squares in 5 or more different ways.

146, 153, 185, 194, 206, 209, 221, 225, 230, 234, 257, 261, 266, 269, 281, 290, 293, 297, 305, 306, 314, 321, 325, 326, 329, 338, 341, 342, 350, 353, 354, 362, 365, 369, 374, 377, 381, 386, 389, 398, 401, 402, 405, 409, 410, 413, 414, 419, 425, 426, 434

Offset: 1

Author

Artur Jasinski, Nov 14 2006

Keywords

• nonn

Examples

			a(1)=146 because 146=9^2+7^2+4^2 = 9^2+8^2+1^2 = 11^2+4^2+3^2 = 11^2+5^2+0^2 = 12^2+1^2+1^2
185=0^2+4^2+13^2=0^2+8^2+11^2=2^2+9^2+10^2=4^2+5^2+12^2=6^2+7^2+10^2, so 185 is in the list.
		

Links

• Ray Chandler, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A124966-A124971.

Programs

Mathematica

Select[Range[434], Length@PowersRepresentations[#, 3, 2] >= 5 &] (* Ray Chandler, Oct 31 2019 *)

PARI

isA124969(n)={ local(cnt=0,z2) ; for(x=0,floor(sqrt(n)), for(y=x,floor(sqrt(n-x^2)), z2=n-x^2-y^2 ; if( z2>=y^2 && issquare(z2), cnt++ ; ) ; if(cnt >=5, return(1) ) ; ) ; ) ; return(0) ; } { for(n=1,800, if( isA124969(n), print1(n,", ") ; ) ; ) ; } \\ R. J. Mathar, Dec 07 2006

Extensions

Corrected and extended by Ray Chandler and R. J. Mathar, Nov 29 2006