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%I A122612 #18 Jun 07 2024 04:05:15
%S A122612 8,16,24,27,32,35,40,43,48,51,54,56,59,62,64,67,70,72,75,78,80,81,83,
%T A122612 86,88,89,91,94,96,97,99,102,104,105,107,108,110,112,113,115,116,118,
%U A122612 120,121,123,124,125,126,128,129,131,132,133,134,135,136,137,139,140,141
%N A122612 Duplicate of A078131.
%C A122612 Previous name was: Sums of cubes of primes.
%C A122612 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 A122612 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 A122612 {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 A122612 (Python)
%o A122612 from sympy import primerange, integer_nthroot as iroot
%o A122612 def ok(n):
%o A122612     cands = [p**3 for p in primerange(2, iroot(n, 3)[0]+1) if p**3 <= n]
%o A122612     return n in cands or any(ok(n-c) for c in cands)
%o A122612 print(list(filter(ok, range(142)))) # _Michael S. Branicky_, Aug 16 2021
%Y A122612 Cf. A000040 (primes), A030078 (cubes of primes), A078130.
%K A122612 dead
%O A122612 1,1
%A A122612 _Jonathan Vos Post_, Sep 20 2006

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