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A122612 Sums of cubes of primes. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
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
LINKS
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.
PROG
(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
CROSSREFS
Cf. A000040 (primes), A030078 (cubes of primes), A078130.
Sequence in context: A229972 A144591 A078131 * A078130 A062171 A048108
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Sep 20 2006
STATUS
approved

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Last modified March 29 08:13 EDT 2024. Contains 371265 sequences. (Running on oeis4.)