OFFSET
1,1
COMMENTS
Definition: Let a number n>1 have prime factorization n=p1^e1*...*pi^ei*..*pm^em, with the primes written in ascending order and the ei>0. If an initial product p1*..*pi is greater than some later prime p(i+1), then n is in the sequence. The definition contains a more restrictive requirement than A289484 does, so it is a proper subsemigroup of A289484. It can be seen that if s and t are in the sequence, the so is s*t. More strongly, if n is in the sequence, so is every multiple of n. Any number in it is divisible by at least 3 primes, although that is not a sufficient condition.
Differs from A212666 first at a(93), because 930=2*3*5*31 is in this sequence but not in A212666. - R. J. Mathar, Sep 02 2018
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
MAPLE
filter:= proc(n) local S, p, i;
S:= sort(convert(numtheory:-factorset(n), list));
p:= 1;
for i from 1 to nops(S)-1 do
p:= p*S[i];
if p > S[i+1] then return true fi;
od;
false
end proc:
select(filter, [$1..1000]); # Robert Israel, Aug 26 2018
KEYWORD
nonn
AUTHOR
Richard Locke Peterson, Aug 16 2017
STATUS
approved