A122612 Duplicate of A078131.

8, 16, 24, 27, 32, 35, 40, 43, 48, 51, 54, 56, 59, 62, 64, 67, 70, 72, 75, 78, 80, 81, 83, 86, 88, 89, 91, 94, 96, 97, 99, 102, 104, 105, 107, 108, 110, 112, 113, 115, 116, 118, 120, 121, 123, 124, 125, 126, 128, 129, 131, 132, 133, 134, 135, 136, 137, 139, 140, 141

Offset: 1

Author

Jonathan Vos Post, Sep 20 2006

Keywords

• dead

Comments

Previous name was: Sums of cubes of primes.

Starts out identical to A078130 (numbers having exactly one representation as sum of cubes>1), until 72. It seems that 154 is the largest integer which cannot be represented as the sum of cubes of primes.

154 is the largest integer that cannot be represented as the sum of cubes of primes. Indeed, every number greater than 154 can be represented as a sum of multiples of 2^3, 3^3, and 5^3. - Giovanni Resta, Jun 16 2016

Crossrefs

Cf. A000040 (primes), A030078 (cubes of primes), A078130.

Programs

Python

from sympy import primerange, integer_nthroot as iroot
def ok(n):
    cands = [p**3 for p in primerange(2, iroot(n, 3)[0]+1) if p**3 <= n]
    return n in cands or any(ok(n-c) for c in cands)
print(list(filter(ok, range(142)))) # Michael S. Branicky, Aug 16 2021

Formula

{A030078} UNION {A030078 + A030078} UNION {A030078 + A030078 + A030078}... = a*8 + b*27 + c*125 + d*343 + e*1331 + f*2197 = a*(p(1))^3 + b*(p(2))^3 + c*(p(3))^3 + d*(p(4))^3 + e*(p(5))^3 + ... where p(i) = A000040(i) and a, b, c, d, e, f, ... are nonnegative integers.