cp's OEIS Frontend

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

%I A062861 #15 Feb 27 2019 03:51:05
%S A062861 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 A062861 55,56,60,61,64,69,77,81,85,86,90,91,92,96,100,105,110,113,121,126,
%U A062861 135,139,140,141,144,145,146,149,154,169,170,174,181,182,190,194,195,196
%N A062861 Numbers which are sums of squares of consecutive numbers (possibly including squares of negative numbers).
%H A062861 Robert Israel, <a href="/A062861/b062861.txt">Table of n, a(n) for n = 0..10000</a>
%H A062861 <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%e A062861 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 A062861 filter:= proc(n)
%p A062861   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 A062861     numtheory:-divisors(6*n))
%p A062861 end proc:
%p A062861 filter(0):= true:
%p A062861 select(filter, [$0..200]); # _Robert Israel_, Jan 22 2017
%t A062861 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 A062861 filterQ[0] = True;
%t A062861 Select[Range[0, 200], filterQ] (* _Jean-François Alcover_, Feb 27 2019, after _Robert Israel_ *)
%o A062861 (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 A062861 Cf. A034705, A062862, A062863.
%K A062861 nonn
%O A062861 0,3
%A A062861 _Henry Bottomley_, Jun 25 2001