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

Author

Lamine Ngom, Apr 14 2021

Keywords

• nonn
• easy

Comments

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

Examples

			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.
		

Crossrefs

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

Programs

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

Formula

Union of A000217 and A126200.