A140999 Members of A067128 that are the smallest numbers with their prime signatures.

1, 2, 4, 6, 8, 12, 24, 30, 36, 48, 60, 72, 96, 120, 180, 240, 360, 420, 480, 720, 840, 1080, 1260, 1440, 1680, 2160, 2520, 3360, 4320, 4620, 5040, 7560, 9240, 10080, 12600, 13860, 15120, 18480, 20160, 25200, 27720, 30240, 36960, 37800, 40320, 45360

Offset: 1

Author

J. Lowell, Jul 28 2008

Keywords

• nonn

Comments

Includes all members of A002182.

Conjecture (false!): includes all members of A094348.

Contribution from Matthew Vandermast, Oct 10 2008: (Start)

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.

Intersection of A067128 and A025487.

Includes all members of A097212. (End)

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000

Programs

Mathematica

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 *)

Extensions

More terms from Matthew Vandermast, Oct 10 2008, Oct 14 2008