

A089016


Largest nround number.


3



2, 30, 1260, 60060, 2042040, 446185740, 25878772920, 7420738134810, 304250263527210, 52331045326680120, 9223346738827371150, 1922760350154212639070, 469153525437627883933080
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OFFSET

0,1


COMMENTS

A positive integer m is said to be nround if it is divisible by all primes p satisfying p^(n+1) < m, or equivalently if all positive integers t < m satisfying GCD(t,m)=1 are divisible by at most n primes (counting multiplicities). Using the fact that p_(t+1)<2*p_t (p_t the (t)th prime) it is easy to prove that there are only finitely many nround numbers for each n. 1round numbers are usually called very round (A048597).


LINKS

T. D. Noe, Table of n, a(n) for n=0..100


EXAMPLE

a(4)=2042040 as follows. Certainly it is 4round since it is <= 19^5 and divisible by all primes < 19. Also it is > 17^5, hence the largest 4round number must be a multiple of 510510 = 2.3.5.7.11.13.17. But no 4round number can be > 19^5 (since it is easy to prove that if p is a prime >= 19 and q is the next prime after p then 2.3.5....p > q^5 ). Thus 2042040, being the largest multiple of 510510 which is <= 19^5, must be the largest 4round number.


MATHEMATICA

Table[k=1; While[prod=Times@@Prime[Range[k]]; prod<Prime[k+1]^(n+1), k++ ]; prod=prod/Prime[k]; prod*Floor[Prime[k]^(n+1)/prod], {n, 0, 100}] (* T. D. Noe, Sep 21 2006 *)


CROSSREFS

Cf. A048597, A122936 (2round numbers), A122937 (3round numbers).
Sequence in context: A350719 A140174 A246741 * A262004 A132104 A208093
Adjacent sequences: A089013 A089014 A089015 * A089017 A089018 A089019


KEYWORD

easy,nonn


AUTHOR

Paul Boddington, Nov 04 2003


EXTENSIONS

More terms from T. D. Noe, Sep 21 2006


STATUS

approved



