A094906 - OEIS

A094906

Numbers m such that m^3-k^3 is a square for some k<m.

1, 4, 8, 9, 10, 14, 16, 25, 28, 32, 33, 36, 40, 49, 56, 57, 64, 65, 71, 72, 74, 78, 81, 90, 100, 105, 112, 114, 121, 126, 128, 130, 132, 140, 144, 148, 154, 155, 160, 169, 176, 193, 196, 200, 217, 218, 224, 225, 228, 250, 252, 256, 260, 266, 273, 280, 284, 288

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..1000

Amiram Eldar, Plot of a(n)/n^(3/2) for n = 1..1000

FORMULA

a(n) seems to be asymptotic to c*n^(3/2) where c = 0.49....

EXAMPLE

8^3-7^3 = 13^2 hence 8 is in the sequence.

MATHEMATICA

q[n_] := AnyTrue[Range[0, n - 1], IntegerQ@Sqrt[n^3 - #^3] &]; Select[Range[300], q] (* Amiram Eldar, May 08 2022 *)