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

2, 5, 6, 10, 13, 14, 15, 19, 28, 29, 30, 31, 35, 41, 44, 50, 54, 55, 56, 60, 61, 69, 77, 85, 86, 90, 91, 92, 96, 105, 110, 113, 126, 135, 139, 140, 141, 145, 146, 149, 154, 170, 174, 181, 182, 190, 194, 195, 199, 203, 204, 205, 209, 218, 221, 230, 231

Offset: 1

Author

Max Alekseyev, Apr 26 2012

Keywords

• nonn

Comments

Nonsquare terms of A062861.

Subsequence of A212016.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A062861, A212016.

Programs

Maple

filter:= proc(n)
  not issqr(n) and
  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:
select(filter, [$1..1000]); # Robert Israel, Jan 22 2017

Mathematica

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#)]&];
Select[Range[1000], filterQ] (* Jean-François Alcover, Jun 08 2020, after Maple *)