OFFSET
1,2
COMMENTS
This sequence is a monoid under multiplication, since if x and y are terms in the sequence and p < x/log(x), then p < xy/log(xy). However, if a term in the sequence is multiplied by a number outside the sequence, the result need not be in the sequence.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
1 is in the sequence because no primes divide 1, 2 is in the sequence since 2 divides 2 and 2 < 2/log(2) ~ 2.9, but 10 is not in the sequence since 5 divides 10 and 5 is not less than 10/log(10) ~ 4.34.
MAPLE
filter:= n -> is(max(numtheory:-factorset(n))<n/ln(n)):
filter(1):= true:
select(filter, [$1..200]); # Robert Israel, Oct 21 2021
MATHEMATICA
ok[n_] := AllTrue[First /@ FactorInteger[n], # Log[n] <= n &]; Select[ Range[120], ok] (* Giovanni Resta, Jun 30 2018 *)
PROG
(PARI) isok(n) = my(f=factor(n)); for (k=1, #f~, if (f[k, 1] >= n/log(n), return(0))); return (1); \\ Michel Marcus, Jul 02 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Richard Locke Peterson, Jun 29 2018
STATUS
approved