%I #15 Aug 30 2022 04:28:36
%S 1,4,8,9,10,14,16,25,28,32,33,36,40,49,56,57,64,65,71,72,74,78,81,90,
%T 100,105,112,114,121,126,128,130,132,140,144,148,154,155,160,169,176,
%U 193,196,200,217,218,224,225,228,250,252,256,260,266,273,280,284,288
%N Numbers m such that m^3-k^3 is a square for some k<m.
%H Amiram Eldar, <a href="/A094906/b094906.txt">Table of n, a(n) for n = 1..1000</a>
%H Amiram Eldar, <a href="/A094906/a094906.jpg">Plot of a(n)/n^(3/2) for n = 1..1000</a>
%F a(n) seems to be asymptotic to c*n^(3/2) where c = 0.49....
%e 8^3-7^3 = 13^2 hence 8 is in the sequence.
%t q[n_] := AnyTrue[Range[0, n - 1], IntegerQ@Sqrt[n^3 - #^3] &]; Select[Range[300], q] (* _Amiram Eldar_, May 08 2022 *)
%o (PARI) for(n=1,420,if(sum(i=0,n-1,issquare(n^3-i^3))>0,print1(n,",")))
%K nonn
%O 1,2
%A _Benoit Cloitre_, Jun 16 2004