A025340 Numbers that are the sum of 3 distinct nonzero squares in exactly 2 ways.

62, 69, 74, 77, 86, 89, 90, 94, 98, 105, 117, 122, 125, 129, 131, 138, 141, 150, 154, 155, 158, 165, 166, 170, 179, 181, 195, 197, 201, 203, 210, 213, 217, 218, 225, 227, 229, 233, 238, 241, 242, 246, 248, 249, 250, 259, 273, 274, 275, 276, 282, 296, 297, 301, 308, 310

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..1777
• Index entries for sequences related to sums of squares

Crossrefs

Subsequence of A004432. Subsequence of A024804.

Programs

Maple

N:= 10^6;
A:= Vector(N):
for a from 1 to floor(sqrt(N/3)) do
  for b from a+1 to floor(sqrt((N-a^2)/2)) do
    c:= [$(b+1) .. floor(sqrt(N-a^2-b^2))]:
    v:= map(t -> a^2 + b^2 + t^2, c):
    A[v]:= map(`+`,A[v],1)
od od:
select(t -> A[t]=2,[$1..N]); # Robert Israel, Jan 03 2016

Mathematica

upperbound = 10^4; max = Floor@Sqrt@upperbound;
range = ConstantArray[0, 3*max^2];
++range[[#]]&/@(Plus@@#&/@Subsets[Range@max^2,{3}]);
Select[Flatten@Position[range, 2], # <= upperbound &] (* Hans Rudolf Widmer, Aug 04 2021 *)