login
A343409
Numbers whose square is the sum of one or more consecutive nonnegative cubes.
0
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).
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
KEYWORD
nonn,easy
AUTHOR
Lamine Ngom, Apr 14 2021
STATUS
approved