A211167 Neither a cube nor the sum of a prime and a positive cube.

2, 5, 7, 9, 16, 17, 22, 23, 26, 28, 33, 35, 36, 41, 43, 47, 52, 53, 57, 59, 63, 65, 73, 76, 78, 82, 85, 89, 92, 96, 99, 103, 112, 113, 118, 119, 120, 122, 126, 129, 133, 141, 146, 149, 151, 155, 160, 163, 169, 170, 179, 183, 185, 188, 193, 197

Offset: 1

Author

Charles R Greathouse IV, Feb 19 2013

Keywords

• nonn

Comments

Hardy & Littlewood's conjecture that this sequence is finite (Conjecture L, p. 51).

Up to 4*10^9 there are 7050 such numbers, the last one being 78526384. - Giovanni Resta, Feb 20 2013

Links

• Giovanni Resta, Table of n, a(n) for n = 1..7050
• G. H. Hardy and J. E. Littlewood, Some problems of 'Partitio numerorum'; III: on the expression of a number as a sum of primes, Acta Mathematica, Vol. 44, pp. 1-70, 1923.

Crossrefs

Cf. A045911.

Programs

PARI

is(n)=if(ispower(n,3),return(0));for(k=1,n^(1/3),if(isprime(n-k^3), return(0)));1