A151925 Write n as a sum of positive squares a^2+b^2+c^2+... with gcd(a,b,...) = 1; a(n) = minimal number of squares needed.

1, 2, 3, 4, 2, 3, 4, 5, 3, 2, 3, 4, 2, 3, 4, 5, 2, 3, 3, 4, 3, 3, 4, 5, 2, 2, 3, 4, 2, 3, 4, 5, 3, 2, 3, 4, 2, 3, 4, 5, 2, 3, 3, 4, 3, 3, 4, 5, 3, 2, 3, 4, 2, 3, 4, 5, 3, 2, 3, 4, 2, 3, 4, 5, 2, 3, 3, 4, 3, 3, 4, 5, 2, 2, 3, 4, 3, 3, 4, 5, 3, 2, 3, 4, 2, 3, 4, 5, 2, 3, 3, 4, 3, 3, 4, 5, 2, 3, 3

Offset

1,2

Comments

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

References

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.

Links

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

N. J. A. Sloane, Fortran program

Example

..... 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

Crossrefs

Sequence in context: A262304 A333609 A273149 * A106653 A173524 A049865

Adjacent sequences: A151922 A151923 A151924 * A151926 A151927 A151928

Keyword

nonn

Author

N. J. A. Sloane and Vinay Vaishampayan, Aug 06 2009, Aug 07 2009

Status

approved