A062861 Numbers which are sums of squares of consecutive numbers (possibly including squares of negative numbers).

0, 1, 2, 4, 5, 6, 9, 10, 13, 14, 15, 16, 19, 25, 28, 29, 30, 31, 35, 36, 41, 44, 49, 50, 54, 55, 56, 60, 61, 64, 69, 77, 81, 85, 86, 90, 91, 92, 96, 100, 105, 110, 113, 121, 126, 135, 139, 140, 141, 144, 145, 146, 149, 154, 169, 170, 174, 181, 182, 190, 194, 195, 196

Offset: 0

Author

Henry Bottomley, Jun 25 2001

Keywords

• nonn

Examples

			13, 14, 15 and 16 are in the sequence since 13 = 2^2 + 3^2, 14 = 1^2 + 2^2 + 3^2, 15 = (-1)^2 + 0^2 + 1^2 + 2^2 + 3^2 and 16 = 4^2.
		

Links

• Robert Israel, Table of n, a(n) for n = 0..10000
• Index entries for sequences related to sums of squares

Crossrefs

Cf. A034705, A062862, A062863.

Programs

Maple

filter:= proc(n)
  ormap(k -> issqr(-3*k^4+3*k^2+36*k*n) and  ((3*k-3*k^2+sqrt(-3*k^4+3*k^2+36*k*n))/(6*k))::integer,
    numtheory:-divisors(6*n))
end proc:
filter(0):= true:
select(filter, [$0..200]); # Robert Israel, Jan 22 2017

Mathematica

filterQ[n_] := AnyTrue[Divisors[6n], IntegerQ[Sqrt[-3#^4 + 3#^2 + 36#*n]] && IntegerQ[(3# - 3#^2 + Sqrt[-3#^4 + 3#^2 + 36#*n])/(6#)]&];
filterQ[0] = True;
Select[Range[0, 200], filterQ] (* Jean-François Alcover, Feb 27 2019, after Robert Israel *)

PARI

{ isA062861(t) = fordiv(6*t,k, z=(k^2-1)/3; if(issquare(4*t/k-z), return(k)); if(z>4*t/k,break); ); 0 } \\ Max Alekseyev, Apr 26 2012