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%I #36 Jun 24 2023 04:14:03
%S 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,
%T 102,105,110,114,120,126,130,132,138,140,150,154,156,165,168,170,174,
%U 180,182,186,190,195,198,204,210,330,390,420,462,510,546,570,630,660
%N Numbers having no fewer distinct prime factors than any predecessor; a(1) = 1.
%C A001221(a(n)) <= A001221(a(n+1));
%C A002110 is a subsequence.
%C The unitary version of Ramanujan's largely composite numbers (A067128), numbers having no fewer unitary divisors than any predecessor. - _Amiram Eldar_, Jun 08 2019
%C Called omega-largely composite numbers by Erdős and Nicolas (1981). - _Amiram Eldar_, Jun 24 2023
%H Amiram Eldar, <a href="/A116998/b116998.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..2500 from Alois P. Heinz)
%H Paul Erdős and Jean-Louis Nicolas, <a href="https://static.renyi.hu/~p_erdos/1981-34.pdf">Sur la fonction: nombre de facteurs premiers de n</a>, L'Enseignement Math., Vol. 27 (1981), pp. 3-27; <a href="http://math.univ-lyon1.fr/~nicolas/ensmathErdos81.pdf">alternative link</a>.
%p a:= proc(n) option remember; local k, t;
%p t:= nops(ifactors(a(n-1))[2]);
%p for k from 1+a(n-1) while nops(ifactors(k)[2])<t do od; k
%p end: a(1):=1:
%p seq(a(n), n=1..80); # _Alois P. Heinz_, Oct 05 2012
%t 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 *)
%Y Cf. A029744, A067128.
%Y Cf. A001221 (omega), A002110 (primorial numbers).
%K nonn
%O 1,2
%A _Reinhard Zumkeller_, Apr 03 2006
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