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%I #8 Jun 20 2019 09:09:33
%S 1,2,4,6,8,12,24,30,36,48,60,72,96,120,180,240,360,420,480,720,840,
%T 1080,1260,1440,1680,2160,2520,3360,4320,4620,5040,7560,9240,10080,
%U 12600,13860,15120,18480,20160,25200,27720,30240,36960,37800,40320,45360
%N Members of A067128 that are the smallest numbers with their prime signatures.
%C Includes all members of A002182.
%C Conjecture (false!): includes all members of A094348.
%C Contribution from _Matthew Vandermast_, Oct 10 2008: (Start)
%C Counterexample to conjecture: 5354228880, the smallest positive multiple of the first 23 positive integers, does not belong to A067128. It is the smallest member of A003418 (a subsequence of A094348) not to be largely composite.
%C Intersection of A067128 and A025487.
%C Includes all members of A097212. (End)
%H Amiram Eldar, <a href="/A140999/b140999.txt">Table of n, a(n) for n = 1..1000</a>
%e 3 doesn't qualify because it's not the smallest number with its prime signature. 16 does not qualify because it's not a member of A067128.
%t PrimeExponents[n_] := Last /@ FactorInteger[n]; lpe = {}; ln = {1};dm=1; Do[d=DivisorSigma[0,n]; If[d>=dm, dm=d; pe = Sort@PrimeExponents@n; If[ FreeQ[lpe, pe], AppendTo[lpe, pe]; AppendTo[ln, n]]], {n, 2, 50000}]; ln (* _Amiram Eldar_, Jun 20 2019 after _Robert G. Wilson v_ at A025487 *)
%K nonn
%O 1,2
%A _J. Lowell_, Jul 28 2008
%E More terms from _Matthew Vandermast_, Oct 10 2008, Oct 14 2008
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