A116998 Numbers having no fewer distinct prime factors than any predecessor; a(1) = 1.

1, 2, 3, 4, 5, 6, 10, 12, 14, 15, 18, 20, 21, 22, 24, 26, 28, 30, 42, 60, 66, 70, 78, 84, 90, 102, 105, 110, 114, 120, 126, 130, 132, 138, 140, 150, 154, 156, 165, 168, 170, 174, 180, 182, 186, 190, 195, 198, 204, 210, 330, 390, 420, 462, 510, 546, 570, 630, 660

Offset: 1

Author

Reinhard Zumkeller, Apr 03 2006

Keywords

• nonn
• look

Comments

A001221(a(n)) <= A001221(a(n+1));

A002110 is a subsequence.

The unitary version of Ramanujan's largely composite numbers (A067128), numbers having no fewer unitary divisors than any predecessor. - Amiram Eldar, Jun 08 2019

Called omega-largely composite numbers by Erdős and Nicolas (1981). - Amiram Eldar, Jun 24 2023

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..2500 from Alois P. Heinz)
• Paul Erdős and Jean-Louis Nicolas, Sur la fonction: nombre de facteurs premiers de n, L'Enseignement Math., Vol. 27 (1981), pp. 3-27; alternative link.

Crossrefs

Cf. A029744, A067128.

Cf. A001221 (omega), A002110 (primorial numbers).

Programs

Maple

a:= proc(n) option remember; local k, t;
      t:= nops(ifactors(a(n-1))[2]);
      for k from 1+a(n-1) while nops(ifactors(k)[2])Alois P. Heinz, Oct 05 2012

Mathematica

a[1] = 1; a[n_] := a[n] = For[nu = PrimeNu[a[n-1]]; k = a[n-1]+1, True, k++, If[PrimeNu[k] >= nu, Return[k]]]; Array[a, 80] (* Jean-François Alcover, Apr 11 2017 *)