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

Author

Reinhard Zumkeller, Nov 19 2002

Keywords

• nonn
• fini
• full

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

• 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.