A212016 -id:A212016 - cp's OEIS frontend

A174069 Numbers that can be written as a sum of at least 2 squares of consecutive positive integers.

5, 13, 14, 25, 29, 30, 41, 50, 54, 55, 61, 77, 85, 86, 90, 91, 110, 113, 126, 135, 139, 140, 145, 149, 174, 181, 190, 194, 199, 203, 204, 221, 230, 245, 255, 265, 271, 280, 284, 285, 294, 302, 313, 330, 355, 365, 366, 371, 380, 384, 385, 415, 421, 434, 446, 451

Offset: 1

Vladimir Joseph Stephan Orlovsky, Mar 06 2010

Numbers are listed without multiplicity: 365 is the first term that is the sum of two or more squares in more than one way. See A062681 for other numbers of that form. - M. F. Hasler, Dec 22 2013

A subsequence of A212016. This sequence focuses on the squares of consecutive positive integers. - Altug Alkan, Dec 24 2015

			5 = 1^2 + 2^2
13 = 2^2 + 3^2
14 = 1^2 + 2^2 + 3^2
25 = 3^2 + 4^2

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A111774, A138591, A151557 (subset of squares), A163251 (subset of primes).

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

Original entry on oeis.org

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

Max Alekseyev, Apr 26 2012

nonn

Nonsquare terms of A062861.

Subsequence of A212016.

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

Cf. A062861, A212016.

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

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 *)

A212018 Integers m such that m^3 is the sum of two or more consecutive integer squares.

Original entry on oeis.org

1, 11, 26, 47, 65, 66, 109, 921, 935, 1079, 2161, 2820, 2860, 5029, 9105, 10681, 12284, 13156, 16761, 18340, 41921, 43500, 61721, 63765, 64605, 66317, 75130, 99359, 105731, 116180, 122009, 146821, 159371, 218205, 253393, 260165, 264680, 269588, 314919, 403130, 404326, 420365

Offset: 1

Max Alekseyev, Apr 26 2012

nonn

Integers m such that m^3 belongs to A212016.

Are there any squares besides 1 in this sequence?

Xianwen Wang, Table of n, a(n) for n = 1..146 (all terms up to 10^10).

Subsequence of A212017.

Cf. A062861, A212015, A212016.

a(39)-a(42) from Xianwen Wang, May 23 2025

A182379 Positive integers n such that n^2 is the sum of two or more consecutive integer squares.

Original entry on oeis.org

1, 5, 11, 29, 34, 38, 39, 50, 55, 70, 77, 88, 92, 94, 105, 106, 115, 135, 138, 143, 155, 158, 169, 182, 185, 189, 195, 242, 245, 253, 274, 284, 316, 321, 332, 356, 357, 385, 413, 430, 440, 495, 511, 531, 650, 652, 655, 671, 676, 679, 724, 726, 764

Offset: 1

Max Alekseyev, Apr 26 2012

nonn

Integers n such that n^2 belongs to A212016.

{ a(n)^2 : n=1,2,... } forms the set difference of A212016 and A212015.

Cf. A062861, A212017, A212018.

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A174069 Numbers that can be written as a sum of at least 2 squares of consecutive positive integers.

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

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A212018 Integers m such that m^3 is the sum of two or more consecutive integer squares.

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A182379 Positive integers n such that n^2 is the sum of two or more consecutive integer squares.

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