A213519 Numbers that are the sum of cubes of distinct primes.

0, 8, 27, 35, 125, 133, 152, 160, 343, 351, 370, 378, 468, 476, 495, 503, 1331, 1339, 1358, 1366, 1456, 1464, 1483, 1491, 1674, 1682, 1701, 1709, 1799, 1807, 1826, 1834, 2197, 2205, 2224, 2232, 2322, 2330, 2349, 2357, 2540, 2548, 2567, 2575, 2665, 2673, 2692

Offset: 1

Author

T. D. Noe, Jul 10 2012

Keywords

• nonn
• easy

Comments

The complement of this sequence is conjectured to have 483370 terms, the last one being 1866000 = A121571(3).

This conjecture was proved by Fuller and Nichols (see the link). - Robert Nichols, Sep 17 2017

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000
• C. Fuller and R. H. Nichols Jr., Generalized Anti-Waring Numbers, J. Int. Seq. 18, 2015, #15.10.5.

Crossrefs

Cf. A121571.

Programs

Mathematica

lim = PrimePi[17]; s = {0}; Do[p = Prime[n]; s = Union[s, s + p^3], {n, lim}]; Select[s, # <= Prime[lim]^3 &]