A161882 Smallest k such that n^2 = a_1^2 + ... + a_k^2 and all a_i are positive integers less than n.

4, 3, 4, 2, 3, 3, 4, 3, 2, 3, 3, 2, 3, 2, 4, 2, 3, 3, 2, 3, 3, 3, 3, 2, 2, 3, 3, 2, 2, 3, 4, 3, 2, 2, 3, 2, 3, 2, 2, 2, 3, 3, 3, 2, 3, 3, 3, 3, 2, 2, 2, 2, 3, 2, 3, 3, 2, 3, 2, 2, 3, 3, 4, 2, 3, 3, 2, 3, 2, 3, 3, 2, 2, 2, 3, 3, 2, 3, 2, 3, 2, 3, 3, 2, 3, 2, 3, 2, 2, 2, 3, 3, 3, 2, 3, 2, 3, 3, 2, 2, 2, 3, 2, 2, 2

Offset: 2

Author

Dmitry Kamenetsky, Jun 21 2009

Keywords

• nonn

Comments

Related to hypotenuse numbers: A161882(A009003(n))=2 for all n.

Jacobi's four-square theorem can be used to show that a(n) <= 4. - Charles R Greathouse IV, Jul 31 2011

Examples

			2^2 = 1^2 + 1^2 + 1^2 + 1^2, so a(2)=4.
3^2 = 2^2 + 2^2 + 1^2, so a(3)=3.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 2..700
• Jean-Charles Meyrignac, Computing minimal equal sums of like powers.
• Eric Weisstein's World of Mathematics, Diophantine Equation 2nd Powers.

Crossrefs

Cf. A161883, A161884, A161885.

Programs

Mathematica

f[n_, k_] := Select[PowersRepresentations[n^2, k, 2], AllTrue[#, 0<#Jean-François Alcover, Oct 03 2020 *)

PARI

A161882(n)={vecmin(factor(n)[,1]%4)==1 && return(2);  if(n==1<M. F. Hasler, Dec 17 2014

Formula

a(n)=2 iff n is in A009003 (hypotenuse numbers), a(n)=4 iff n is in A000079 (powers of 2), otherwise a(n)=3. - M. F. Hasler, Dec 17 2014

Extensions

More terms from Alois P. Heinz, Dec 04 2014