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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
OFFSET
0,3
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
KEYWORD
nonn
AUTHOR
Henry Bottomley, Jun 25 2001
STATUS
approved