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

1,1

Comments

Nonsquare terms of A062861.

Subsequence of A212016.

Links

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

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 *)

Crossrefs

Cf. A062861, A212016.

Sequence in context: A187231 A162340 A212016 * A255341 A089269 A047440

Adjacent sequences: A212012 A212013 A212014 * A212016 A212017 A212018

Keyword

nonn

Author

Max Alekseyev, Apr 26 2012

Status

approved