A343409 - OEIS

%I #28 Sep 12 2023 02:08:30

%S 0,1,3,6,8,10,15,21,27,28,36,45,55,64,66,78,91,105,120,125,136,153,

%T 171,190,204,210,216,231,253,276,300,312,315,323,325,343,351,378,406,

%U 435,465,496,504,512,528,561,588,595,630,666,703,720,729,741,780,820

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

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

%F Union of A000217 and A126200.

%e 8 is a term because 8^2 = 64 = 4^3.

%e 10 is a term because 10^2 = 100 = 1^3 + 2^3 + 3^3 + 4^3.

%p N:= 1000: # for terms <= N

%p M:= floor(N^(2/3)):

%p S:= [seq(n^2*(n+1)^2/4, n=0..M)]:

%p SD:= {0,seq(seq(S[i]-S[j],j=1..i-1),i=1..M+1)}:

%p Q:= select(t -> t <= N^2 and issqr(t),SD):

%p sort(convert(map(sqrt,Q),list)); # _Robert Israel_, Sep 11 2023

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

%K nonn,easy

%O 1,3

%A _Lamine Ngom_, Apr 14 2021