A124968 Numbers which can be expressed as the ordered sum of 3 squares in 4 or more different ways.
81, 89, 101, 125, 129, 134, 146, 149, 153, 161, 162, 170, 171, 173, 185, 189, 194, 198, 201, 206, 209, 221, 225, 230, 233, 234, 241, 242, 243, 245, 246, 249, 250, 251, 254, 257, 261, 266, 269, 270, 274, 278, 281, 285, 289, 290, 293, 294, 297, 299, 305, 306
Offset: 1
Keywords
Examples
a(1)=81 because 81 = 6^2 + 6^2 + 3^2 = 7^2 + 4^2 + 4^2 = 8^2 + 4^2 + 1^2 = 9^2 + 0^2 + 0^2. 161 = 1^2 + 4^2 + 12^2 = 2^2 + 6^2 + 11^2 = 4^2 + 8^2 + 9^2 = 5^2 + 6^2 + 10^2, so 161 is in the list.
Links
- Robert Price, Table of n, a(n) for n = 1..81953
Programs
-
Mathematica
Select[Range[310], Length@PowersRepresentations[#, 3, 2] >= 4 &] (* Ray Chandler, Oct 31 2019 *)
-
PARI
isA124968(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 >=4, return(1) ) ; ) ; ) ; return(0) ; } { for(n=1,800, if( isA124968(n), print1(n,", ") ; ) ; ) ; } \\ R. J. Mathar
Extensions
Corrected and extended by Ray Chandler and R. J. Mathar, Nov 29 2006
Comments