A025321 Numbers that are the sum of 3 nonzero squares in exactly 1 way.

3, 6, 9, 11, 12, 14, 17, 18, 19, 21, 22, 24, 26, 29, 30, 34, 35, 36, 42, 43, 44, 45, 46, 48, 49, 50, 53, 56, 61, 65, 67, 68, 70, 72, 73, 76, 78, 82, 84, 88, 91, 93, 96, 97, 104, 106, 109, 115, 116, 120, 133, 136, 140, 142, 144, 145, 157, 163, 168, 169, 172, 176, 180, 184, 190

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

It appears that all terms have the form 4^i A094740(j) for some i and j. - T. D. Noe, Jun 06 2008

This is true, because A025427(4*n) = A025427(n) for all n. - Robert Israel, Mar 09 2016

Links

• Donovan Johnson, Table of n, a(n) for n = 1..605 (terms < 10^8; first 417 terms from T. D. Noe)
• Eric Weisstein's World of Mathematics, Square Number.
• Index entries for sequences related to sums of squares

Crossrefs

Cf. A000408, A025427, A243148.

Programs

Mathematica

lim=20; nLst=Table[0, {lim^2}]; Do[n=a^2+b^2+c^2; If[n>0 && nT. D. Noe, Jun 06 2008 *)
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, 3], {n, 0, 200}], 1] - 1 // Flatten (* Jean-François Alcover, Nov 06 2020, after Alois P. Heinz in A243148 *)

PARI

is(n)=if(n<11, return(n>0 && n%3==0)); if(n%4==0, return(is(n/4))); my(w); for(i=sqrtint((n-1)\3)+1,sqrtint(n-2), my(t=n-i^2); for(j=sqrtint((t-1)\2)+1,min(sqrtint(t-1),i), if(issquare(t-j^2), w++>1 && return(0)))); w \\ Charles R Greathouse IV, Aug 05 2024

Formula

A243148(a(n),3) = 1. - Alois P. Heinz, Feb 25 2019