

A316350


Positive integers x that are (x1)/log(x1) smooth, that is, if a prime p divides x, then p <= (x1)/log(x1).


0



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, 50, 52, 54, 55, 56, 60, 63, 64, 65, 66, 70, 72, 75, 77, 78, 80, 81, 84, 85, 88, 90, 91, 95, 96, 98, 99, 100, 102, 104, 105, 108, 110, 112, 114, 115, 117, 119, 120
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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

Table of n, a(n) for n=1..63.


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.


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

Cf. A050500.
Sequence in context: A138969 A161819 A244799 * A071562 A241562 A100345
Adjacent sequences: A316347 A316348 A316349 * A316351 A316352 A316353


KEYWORD

nonn


AUTHOR

Richard Locke Peterson, Jun 29 2018


STATUS

approved



