A025284 Numbers that are the sum of 2 nonzero squares in exactly 1 way.

2, 5, 8, 10, 13, 17, 18, 20, 25, 26, 29, 32, 34, 37, 40, 41, 45, 52, 53, 58, 61, 68, 72, 73, 74, 80, 82, 89, 90, 97, 98, 100, 101, 104, 106, 109, 113, 116, 117, 122, 128, 136, 137, 146, 148, 149, 153, 157, 160, 162, 164, 169, 173, 178, 180, 181, 193, 194, 197, 202, 208, 212

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

A025426(a(n)) = 1. - Reinhard Zumkeller, Aug 16 2011

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Square Number
• G. Xiao, Two squares
• Index entries for sequences related to sums of squares

Crossrefs

Cf. A000404, A025426, A081324, A125022, A018825, A001481, A007692, A243148.

Programs

Haskell

import Data.List (elemIndices)
a025284 n = a025284_list !! (n-1)
a025284_list = elemIndices 1 a025426_list
-- Reinhard Zumkeller, Aug 16 2011

Mathematica

selQ[n_] := Length[ Select[ PowersRepresentations[n, 2, 2], Times @@ # != 0 &]] == 1; Select[Range[300], selQ] (* Jean-François Alcover, Oct 03 2013 *)
b[n_, i_, k_, t_] := b[n, i, k, t] = If[n == 0, If[t == 0, 1, 0], If[i<1 || t<1, 0, b[n, i - 1, k, t] + If[i^2 > n, 0, b[n - i^2, i, k, t - 1]]]];
T[n_, k_] := b[n, Sqrt[n] // Floor, k, k];
Position[Table[T[n, 2], {n, 0, 300}], 1] - 1 // Flatten (* Jean-François Alcover, Nov 06 2020, after Alois P. Heinz in A243148 *)

Formula

A243148(a(n),2) = 1. - Alois P. Heinz, Feb 25 2019