A134738 Cubes which are not the sum of three squares.

343, 3375, 12167, 21952, 29791, 59319, 103823, 166375, 216000, 250047, 357911, 493039, 658503, 778688, 857375, 1092727, 1367631, 1404928, 1685159, 1906624, 2048383, 2460375, 2924207, 3442951, 3796416, 4019679, 4657463, 5359375

Offset: 1

Author

Artur Jasinski, Nov 07 2007

Keywords

• nonn

Comments

This sequence was inspired by e-mail from Ray Chandler, Nov 07 2007

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A004215, A134739.

Programs

Maple

N:= 10^10: # to get all terms <= N
sort([seq(seq(4^(3*i) * (8*j + 7)^3, j = 0 .. floor((N^(1/3)/4^i - 7)/8)), i = 0 .. floor(log[4](N^(1/3))))]); # Robert Israel, Dec 26 2017

Mathematica

b = Table[x^3, {x, 1, 300}]; a = {}; Do[Do[Do[AppendTo[a, (x^2 + y^2 + z^2)^3], {x, 0, 30}], {y, 0, 30}], {z, 0, 30}]; Union[a]; Complement[b, a] (*Artur Jasinski*)
Select[Range[200]^3,SquaresR[3,#]==0&] (* Harvey P. Dale, Feb 03 2015 *)

Python

def A134738(n):
    def bisection(f,kmin=0,kmax=1):
        while f(kmax) > kmax: kmax <<= 1
        kmin = kmax >> 1
        while kmax-kmin > 1:
            kmid = kmax+kmin>>1
            if f(kmid) <= kmid:
                kmax = kmid
            else:
                kmin = kmid
        return kmax
    def f(x): return n+x-sum(((x>>(i<<1))-7>>3)+1 for i in range(x.bit_length()>>1))
    return bisection(f,n,n)**3 # Chai Wah Wu, Feb 14 2025

Formula

a(n) = A004215(n)^3. - Ray Chandler, Jan 29 2009

Extensions

Extended by Ray Chandler, Jan 29 2009