A062861 - OEIS

%I #15 Feb 27 2019 03:51:05

%S 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,

%T 55,56,60,61,64,69,77,81,85,86,90,91,92,96,100,105,110,113,121,126,

%U 135,139,140,141,144,145,146,149,154,169,170,174,181,182,190,194,195,196

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

%H Robert Israel, <a href="/A062861/b062861.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>

%e 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.

%p filter:= proc(n)

%p   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,

%p     numtheory:-divisors(6*n))

%p end proc:

%p filter(0):= true:

%p select(filter, [$0..200]); # _Robert Israel_, Jan 22 2017

%t 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#)]&];

%t filterQ[0] = True;

%t Select[Range[0, 200], filterQ] (* _Jean-François Alcover_, Feb 27 2019, after _Robert Israel_ *)

%o (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

%Y Cf. A034705, A062862, A062863.

%K nonn

%O 0,3

%A _Henry Bottomley_, Jun 25 2001