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A212015 Nonsquare positive integers that are sums of consecutive integer squares.

%I A212015 #15 Jun 08 2020 05:23:04
%S A212015 2,5,6,10,13,14,15,19,28,29,30,31,35,41,44,50,54,55,56,60,61,69,77,85,
%T A212015 86,90,91,92,96,105,110,113,126,135,139,140,141,145,146,149,154,170,
%U A212015 174,181,182,190,194,195,199,203,204,205,209,218,221,230,231
%N A212015 Nonsquare positive integers that are sums of consecutive integer squares.
%C A212015 Nonsquare terms of A062861.
%C A212015 Subsequence of A212016.
%H A212015 Robert Israel, <a href="/A212015/b212015.txt">Table of n, a(n) for n = 1..10000</a>
%p A212015 filter:= proc(n)
%p A212015   not issqr(n) and
%p A212015   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 A212015     numtheory:-divisors(6*n))
%p A212015 end proc:
%p A212015 select(filter, [$1..1000]); # _Robert Israel_, Jan 22 2017
%t A212015 filterQ[n_] := !IntegerQ[Sqrt[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 A212015 Select[Range[1000], filterQ] (* _Jean-François Alcover_, Jun 08 2020, after Maple *)
%Y A212015 Cf. A062861, A212016.
%K A212015 nonn
%O A212015 1,1
%A A212015 _Max Alekseyev_, Apr 26 2012