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A062861 Numbers which are sums of squares of consecutive numbers (possibly including squares of negative numbers). 8
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified July 22 05:47 EDT 2019. Contains 325213 sequences. (Running on oeis4.)