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%I #10 Jul 19 2019 13:54:23
%S 2,3,4,5,6,7,10,11,12,13,14,17,18,19,22,23,26,29,30,31,34,37,38,41,42,
%T 43,46,47,48,53,58,59,61,62,66,67,71,72,73,74,78,79,82,83,86,89,94,97,
%U 101,102,103,106,107,109,113,114,118,120,122,127,131,134,137,138,139
%N Sorted products of primes (2,3,5,7...) and factorials (1,2,6,24...).
%H Robert Israel, <a href="/A098908/b098908.txt">Table of n, a(n) for n = 1..10000</a>
%e In the set of products of primes and factorials 10 (= 5 times factorial 2) is the seventh largest number and therefore is the seventh member of the sequence.
%p N:= 1000: # to get all terms <= N
%p P:= select(isprime, [2,seq(i,i=3..N,2)]):
%p F:= 1: v:= 1:
%p for n from 2 do
%p v:= v*n;
%p if v > N then break fi;
%p F:= F, v;
%p od:
%p F:= {F}:
%p sort(convert(select(`<=`,{seq(seq(p*f, f=F),p=P)},N),list)); # _Robert Israel_, Aug 27 2018
%t With[{upto=140},Select[Union[Flatten[Table[p*f,{p,Prime[ Range[ PrimePi[ upto]]]},{f,Range[10]!}]]],#<=upto&]] (* _Harvey P. Dale_, Jul 19 2019 *)
%Y Cf. A000040, A000142.
%K nonn
%O 1,1
%A _Axel Harvey_, Oct 15 2004
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