

A119748


Numbers that are not the sum of a prime and a (nontrivial, positive) power.


3




OFFSET

1,2


COMMENTS

From a question raised by Tanya Khovanova.
1771561 = 11^6 is the first composite number here.  T. D. Noe, Sep 29 2011
James Van Buskirk and John Robertson report that these are the only terms known up to 10^10.  Charles R Greathouse IV, Jan 30 2014
Hardy & Littlewood's Conjecture H implies that there are finitely many nonsquare terms in this sequence. Wang's result implies that a(n) >> n^1.018.  Charles R Greathouse IV, May 28 2015


REFERENCES

G. H. Hardy, J. E. Littlewood, Some of the problems of partitio numerorum III: On the expression of a large number as a sum of primes, Acta Mathematica 44 (1923), pp. 170.
Wang Tianze, On the exceptional set for the equation n = p + k^2, Acta Mathematica Sinica 11 (1995), pp. 156167.


LINKS

Table of n, a(n) for n=1..5.
John Robertson, Integers of the form x^2+kp (1999)


PROG

(PARI) is(n)=for(e=2, log(n)\log(2), for(b=2, sqrtnint(n, e), if(isprime(nb^e)&&!ispower(b), return(0)))); 1 \\ Charles R Greathouse IV, May 28 2015


CROSSREFS

Cf. A119747.
Sequence in context: A176117 A078748 A051131 * A101341 A079014 A215436
Adjacent sequences: A119745 A119746 A119747 * A119749 A119750 A119751


KEYWORD

nonn,more


AUTHOR

David W. Wilson, Jul 30 2006


EXTENSIONS

1771561 from Max Alekseyev, Jul 31 2006


STATUS

approved



