1,2

Similar to A002828, but only now primitive representations are allowed.

Of course a(n) >= A002828(n).

From Lagrange's theorem, a(n) <= 5 (see also Estermann, Grosswald, Th. 3, p. 176).

Furthermore, it appears (and should be easy to prove) that:

a(n) = 1 iff n=1

a(n) = 2 iff n in A008784\{1}

a(n) = 3 iff n in A151926

a(n) = 4 iff n == 4 or 7 mod 8

a(n) = 5 iff n == 0 mod 8

Estermann, T., On the representations of a number as a sum of squares, Acta Arith., 45 (1937), 93-125.

E. Grosswald, Representations of Integers as Sums of Squares. Springer-Verlag, NY, 1985.

N. J. A. Sloane, Table of n, a(n) for n = 1..1000

N. J. A. Sloane, Fortran program

..... n .. a(n) ..<- Numbers when squared add to n ->

-----------------------------------------------------

......1......1......1

......2......2......1......1

......3......3......1......1......1

......4......4......1......1......1......1

......5......2......1......2

......6......3......1......1......2

......7......4......1......1......1......2

......8......5......1......1......1......1......2

......9......3......1......2......2

.....10......2......1......3

.....11......3......1......1......3

.....12......4......1......1......1......3

.....13......2......2......3

.....14......3......1......2......3

.....15......4......1......1......2......3

.....16......5......1......1......1......2......3

.....17......2......1......4

.....18......3......1......1......4

.....19......3......1......3......3

.....20......4......1......1......3......3

Sequence in context: A162247 A035578 A107795 this_sequence A106653 A049865 A070771

Adjacent sequences: A151922 A151923 A151924 this_sequence A151926 A151927 A151928

nonn

N. J. A. Sloane (njas(AT)research.att.com) and Vinay Vaishampayan (vinay(AT)research.att.com), Aug 06 2009, Aug 07 2009