A078136 Numbers having exactly one representation as sum of squares>1.

4, 8, 9, 12, 13, 17, 18, 21, 22, 26, 27, 30, 31, 35, 39

Offset

1,1

Comments

A078134(a(n))=1.

The sequence is finite with a(15)=39 as last term, since numbers m>39 can be represented as sums of squares>1 (even of squares of primes and even of squares of 2, 3 and 4 and even of squares of 2, 3 and 5) in at least two ways. Proof: if m=40+4k, k>=0, then m=(k+10)*2^2=(k+1)*2^2+4*3^2; if m=41+4k, then m=(k+8)*2^2+3^2=(k+4)*2^2+5^2; if m=42+4k, then m=(k+6)*2^2+2*3^2=(k+2)*2^2+3^2+5^2; if m=43+4k, then m=(k+4)*2^2+3*3^2=k*2^2+2*3^2+5^2. - Hieronymus Fischer, Nov 11 2007

Links

Table of n, a(n) for n=1..15.

Eric Weisstein's World of Mathematics, Square Number.

Index entries for sequences related to sums of squares

Crossrefs

Cf. A000290, A078137, A078135, A078130.

Cf. A078134, A078139, A090677, A078137, A134754, A134755.

Sequence in context: A078137 A294574 A010453 * A291791 A037973 A044844

Adjacent sequences: A078133 A078134 A078135 * A078137 A078138 A078139

Keyword

nonn,fini,full

Author

Reinhard Zumkeller, Nov 19 2002

Status

approved