cp's OEIS Frontend

A316350 Positive integers x that are x/log(x) smooth, that is, if a prime p divides x, then p <= x/log(x).

%I A316350 #26 Oct 25 2021 11:05:15
%S A316350 1,2,4,6,8,9,12,15,16,18,20,24,25,27,28,30,32,35,36,40,42,44,45,48,49,
%T A316350 50,52,54,55,56,60,63,64,65,66,70,72,75,77,78,80,81,84,85,88,90,91,95,
%U A316350 96,98,99,100,102,104,105,108,110,112,114,115,117,119,120
%N A316350 Positive integers x that are x/log(x) smooth, that is, if a prime p divides x, then p <= x/log(x).
%C A316350 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.
%H A316350 Robert Israel, <a href="/A316350/b316350.txt">Table of n, a(n) for n = 1..10000</a>
%e A316350 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.
%p A316350 filter:= n -> is(max(numtheory:-factorset(n))<n/ln(n)):
%p A316350 filter(1):= true:
%p A316350 select(filter, [$1..200]); # _Robert Israel_, Oct 21 2021
%t A316350 ok[n_] := AllTrue[First /@ FactorInteger[n], # Log[n] <= n &]; Select[ Range[120], ok] (* _Giovanni Resta_, Jun 30 2018 *)
%o A316350 (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
%Y A316350 Cf. A050500.
%K A316350 nonn
%O A316350 1,2
%A A316350 _Richard Locke Peterson_, Jun 29 2018