A273318 Numbers n such that n+k-1 is the sum of two nonzero squares in exactly k ways for all k = 1, 2, 3.

58472, 79208, 104616, 150048, 160848, 205648, 224648, 234448, 252808, 259648, 259920, 294048, 297448, 387648, 421648, 433448, 462976, 488448, 506248, 563048, 621448, 683648, 770976, 790848, 799648, 837448, 1008648, 1040848, 1084904, 1186632, 1195648, 1205648, 1212064

Offset: 1

Author

Altug Alkan, May 19 2016

Keywords

• nonn

Comments

Numbers n such that n+k-1 is the sum of two nonzero squares in exactly 4-k ways for all k = 1, 2, 3 are 22984, 65600, 80800, 85544, ...

Examples

			58472 is a term because;
58472 = 86^2 + 226^2.
58473 = 48^2 + 237^2 = 147^2 + 192^2.
58474 = 57^2 + 235^2 = 125^2 + 207^2 = 143^2 + 195^2.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..1095

Crossrefs

Cf. A000404, A025284, A025285, A025286.

Programs

Maple

N:= 10^6: # get all terms <= N-2
R:= Vector(N):
for x from 1 to floor(sqrt(N)) do
  for y from 1 to min(x,floor(sqrt(N-x^2))) do
    R[x^2+y^2]:= R[x^2+y^2]+1
od od:
count:= 0:
for n from 1 to N-2 do
  if [R[n],R[n+1],R[n+2]] = [1,2,3] then
  count:= count+1; A[count]:= n;
fi
od:
seq(A[i],i=1..count); # Robert Israel, May 19 2016

PARI

is(n,k) = {nb = 0; lim = sqrtint(n); for (x=1, lim, if ((n-x^2 >= x^2) && issquare(n-x^2), nb++); ); nb == k; }
isok(n) = is(n,1) && is(n+1,2) && is(n+2,3);