A122612 - OEIS

%I #18 Jun 07 2024 04:05:15

%S 8,16,24,27,32,35,40,43,48,51,54,56,59,62,64,67,70,72,75,78,80,81,83,

%T 86,88,89,91,94,96,97,99,102,104,105,107,108,110,112,113,115,116,118,

%U 120,121,123,124,125,126,128,129,131,132,133,134,135,136,137,139,140,141

%N Duplicate of A078131.

%C Previous name was: Sums of cubes of primes.

%C 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.

%C 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

%F {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.

%o (Python)

%o from sympy import primerange, integer_nthroot as iroot

%o def ok(n):

%o     cands = [p**3 for p in primerange(2, iroot(n, 3)[0]+1) if p**3 <= n]

%o     return n in cands or any(ok(n-c) for c in cands)

%o print(list(filter(ok, range(142)))) # _Michael S. Branicky_, Aug 16 2021

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

%K dead

%O 1,1

%A _Jonathan Vos Post_, Sep 20 2006