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A079870 a(1)=1 and for n>1: ceiling(n^(1/Omega(n))), where Omega(n) is the total number of prime factors of n (A001222).

%I A079870 #15 Oct 28 2024 08:42:30
%S A079870 1,2,3,2,5,3,7,2,3,4,11,3,13,4,4,2,17,3,19,3,5,5,23,3,5,6,3,4,29,4,31,
%T A079870 2,6,6,6,3,37,7,7,3,41,4,43,4,4,7,47,3,7,4,8,4,53,3,8,3,8,8,59,3,61,8,
%U A079870 4,2,9,5,67,5,9,5,71,3,73,9,5,5,9,5,79,3,3,10,83,4,10,10,10,4,89,4,10,5,10
%N A079870 a(1)=1 and for n>1: ceiling(n^(1/Omega(n))), where Omega(n) is the total number of prime factors of n (A001222).
%H A079870 Paolo Xausa, <a href="/A079870/b079870.txt">Table of n, a(n) for n = 1..10000</a>
%F A079870 A079871(n) = a(n)^A001222(n).
%F A079870 a(n) >= A079868(n); A020639(n) <= a(n) <= A006530(n);
%F A079870 a(m) = A079868(m) iff m is a prime power (A000961).
%t A079870 A079870[n_] := If [n == 1, 1, Ceiling[n^(1/PrimeOmega[n])]];
%t A079870 Array[A079870, 100] (* _Paolo Xausa_, Oct 28 2024 *)
%o A079870 (PARI) a(n) = if (n==1, 1, ceil(n^(1/bigomega(n)))); \\ _Michel Marcus_, May 31 2016
%Y A079870 Cf. A001222, A006530, A020639, A068794, A068795, A079869, A079871.
%K A079870 nonn
%O A079870 1,2
%A A079870 _Reinhard Zumkeller_, Jan 13 2003