

A100952


Numbers that cannot be written as p*q+r with three distinct primes p, q and r.


1



1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 24, 30, 36, 42, 60
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OFFSET

1,2


COMMENTS

A100951(a(n)) = 0;
Conjecture: the sequence is complete.
A weaker conjecture: every integer greater than 60 (or some larger value based on further search) may be partitioned into a prime p and a semiprime qr, where the prime p is bounded by log(min(q,r)). Chen (1978) showed that all sufficiently large even numbers are the sum of a prime and the product of at most two primes. Zumkeller's conjecture effectively extends this from "even" to both even and odd integers.  Jonathan Vos Post, Nov 25 2004
Conjecture: Every positive integer can be represented as p*qr with distinct primes p, q, r.  Zak Seidov, Aug 28 2012


REFERENCES

Chen, J.R. "On the Representation of a Large Even Number as the Sum of a Prime and the Product of at Most Two Primes, II." Sci. Sinica 21, 421430, 1978.


LINKS

Table of n, a(n) for n=1..21.


EXAMPLE

A100949(60) = #{11+7*7, 5+5*11, 3+3*19, 2+2*29} = 4, but A100951(60) = 0 as in each partition only 2 primes are used, therefore 60 is a term.


CROSSREFS

Cf. A100949, A100951.
Sequence in context: A117296 A096503 A055238 * A303332 A030477 A178859
Adjacent sequences: A100949 A100950 A100951 * A100953 A100954 A100955


KEYWORD

nonn


AUTHOR

Reinhard Zumkeller, Nov 23 2004


STATUS

approved



