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A316350 Positive integers x that are (x-1)/log(x-1) smooth, that is, if a prime p divides x, then p <= (x-1)/log(x-1). 0

%I

%S 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 50,52,54,55,56,60,63,64,65,66,70,72,75,77,78,80,81,84,85,88,90,91,95,

%U 96,98,99,100,102,104,105,108,110,112,114,115,117,119,120

%N Positive integers x that are (x-1)/log(x-1) smooth, that is, if a prime p divides x, then p <= (x-1)/log(x-1).

%C 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.

%e 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.

%t ok[n_] := AllTrue[First /@ FactorInteger[n], # Log[n] <= n &]; Select[ Range[120], ok] (* _Giovanni Resta_, Jun 30 2018 *)

%o (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 Cf. A050500.

%K nonn

%O 1,2

%A _Richard Locke Peterson_, Jun 29 2018

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Last modified March 18 16:00 EDT 2019. Contains 321292 sequences. (Running on oeis4.)