A343409 Numbers whose square is the sum of one or more consecutive nonnegative cubes.

0, 1, 3, 6, 8, 10, 15, 21, 27, 28, 36, 45, 55, 64, 66, 78, 91, 105, 120, 125, 136, 153, 171, 190, 204, 210, 216, 231, 253, 276, 300, 312, 315, 323, 325, 343, 351, 378, 406, 435, 465, 496, 504, 512, 528, 561, 588, 595, 630, 666, 703, 720, 729, 741, 780, 820

Offset

1,3

Comments

Roots of square terms of A217843. Sequence contains (but is not limited to) cubes (A000578) and triangular numbers (A000217).

Links

Table of n, a(n) for n=1..56.

Formula

Union of A000217 and A126200.

Example

8 is a term because 8^2 = 64 = 4^3.
10 is a term because 10^2 = 100 = 1^3 + 2^3 + 3^3 + 4^3.

Maple

N:= 1000: # for terms <= N
M:= floor(N^(2/3)):
S:= [seq(n^2*(n+1)^2/4, n=0..M)]:
SD:= {0, seq(seq(S[i]-S[j], j=1..i-1), i=1..M+1)}:
Q:= select(t -> t <= N^2 and issqr(t), SD):
sort(convert(map(sqrt, Q), list)); # Robert Israel, Sep 11 2023

Crossrefs

Cf. A000217, A000578, A126200, A163393, A217843.

Sequence in context: A187336 A169582 A121741 * A043549 A228707 A290218

Adjacent sequences: A343406 A343407 A343408 * A343410 A343411 A343412

Keyword

nonn,easy

Author

Lamine Ngom, Apr 14 2021

Status

approved