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