A124967 Numbers which can be expressed as the ordered sum of 3 squares in 3 or more different ways.

41, 50, 54, 65, 66, 74, 81, 86, 89, 90, 98, 99, 101, 110, 113, 114, 117, 121, 122, 125, 126, 129, 131, 134, 137, 145, 146, 149, 150, 153, 161, 162, 164, 166, 169, 170, 171, 173, 174, 178, 179, 181, 182, 185, 186, 189, 194, 197, 198, 200, 201, 205, 206, 209

Offset: 1

Author

Artur Jasinski, Nov 14 2006

Keywords

• nonn

Examples

			a(1) = 41 because 41 = 4^2+4^2+3^2 or 5^2+4^2+0^2 or 6^2+2^2+1^2.
117=0^2+6^2+9^2=1^2+4^2+10^2=2^2+7^2+8^2, so 117 is in the list.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A124966-A124971.

Programs

Maple

b:= proc(n, i, t) option remember; `if`(n=0, 1, `if`(t*i^23, 3, min(3, b(n, i-1, t)+
      `if`(i^2>n, 0, b(n-i^2, i, t-1))))))
    end:
a:= proc(n) option remember; local k;
      for k from 1 +`if`(n=1, 0, a(n-1))
      while b(k, isqrt(k), 3)<3 do od; k
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Apr 10 2013

Mathematica

Select[Range[210], Length@PowersRepresentations[#, 3, 2] >= 3 &] (* Ray Chandler, Oct 31 2019 *)

PARI

isA124967(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 >=3, return(1) ) ; ) ; ) ; return(0) ; } { for(n=1,200, if( isA124967(n), print1(n,", ") ; ) ; ) ; } (Mathar)

Extensions

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