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

1,1

Comments

Subset of A124967.

Links

Robert Price, Table of n, a(n) for n = 1..81953

Example

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.

Mathematica

Select[Range[310], Length@PowersRepresentations[#, 3, 2] >= 4 &] (* Ray Chandler, Oct 31 2019 *)

Prog

(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

Crossrefs

Cf. A124966-A124971.

Sequence in context: A295700 A286898 A184044 * A294577 A044865 A162529

Adjacent sequences: A124965 A124966 A124967 * A124969 A124970 A124971

Keyword

nonn

Author

Artur Jasinski, Nov 14 2006

Extensions

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

Status

approved