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A086568 Smallest number having as many distinct prime factors as n has prime factors, when counted with multiplicity.

%I A086568 #20 Sep 26 2017 11:47:04
%S A086568 1,2,2,6,2,6,2,30,6,6,2,30,2,6,6,210,2,30,2,30,6,6,2,210,6,6,30,30,2,
%T A086568 30,2,2310,6,6,6,210,2,6,6,210,2,30,2,30,30,6,2,2310,6,30,6,30,2,210,
%U A086568 6,210,6,6,2,210,2,6,30,30030,6,30,2,30,6,30,2,2310,2,6,30,30,6,30,2
%N A086568 Smallest number having as many distinct prime factors as n has prime factors, when counted with multiplicity.
%C A086568 a(n) = n if and only if n = A002110(m) for some m. That is, primorials give the fixed points of this sequence.
%H A086568 Antti Karttunen, <a href="/A086568/b086568.txt">Table of n, a(n) for n = 1..2310</a>
%H A086568 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>
%F A086568 a(n) = prime(bigomega(n))# = A002110(A001222(n)).
%F A086568 For all n >= 1, A001221(a(n)) = A001222(a(n)) = A001222(n).
%t A086568 Array[Times @@ Prime@ Range@ PrimeOmega@ # &, 79] (* _Michael De Vlieger_, Sep 25 2017 *)
%o A086568 (PARI)
%o A086568 A002110(n) = prod(i=1,n,prime(i));
%o A086568 A086568(n) = A002110(bigomega(n)); \\ _Antti Karttunen_, Jul 07 2017
%Y A086568 Cf. A001221, A001222, A002110, A130675, A292586.
%K A086568 nonn
%O A086568 1,2
%A A086568 _Reinhard Zumkeller_, Jan 03 2004
%E A086568 Formula corrected and comments edited by _Antti Karttunen_, Jul 07 2017