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

0,3

Links

Robert Israel, Table of n, a(n) for n = 0..10000

Index entries for sequences related to sums of squares

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A034705, A062862, A062863.

Sequence in context: A194469 A143072 A089648 * A120629 A169694 A285163

Adjacent sequences: A062858 A062859 A062860 * A062862 A062863 A062864

Keyword

nonn

Author

Henry Bottomley, Jun 25 2001

Status

approved