cp's OEIS Frontend

A079866 a(1)=1 and for n>1: floor(n^(1/Omega(n))), where Omega(n) is the total number of prime factors of n (A001222).

%I A079866 #18 Dec 08 2022 07:30:17
%S A079866 1,2,3,2,5,2,7,2,3,3,11,2,13,3,3,2,17,2,19,2,4,4,23,2,5,5,3,3,29,3,31,
%T A079866 2,5,5,5,2,37,6,6,2,41,3,43,3,3,6,47,2,7,3,7,3,53,2,7,2,7,7,59,2,61,7,
%U A079866 3,2,8,4,67,4,8,4,71,2,73,8,4,4,8,4,79,2,3,9,83,3,9,9,9,3,89,3,9,4,9,9,9,2
%N A079866 a(1)=1 and for n>1: floor(n^(1/Omega(n))), where Omega(n) is the total number of prime factors of n (A001222).
%C A079866 a(n) <= A079868(n).
%C A079866 A020639(n) <= a(n) <= A006530(n);
%C A079866 a(m) = A079868(m) = A079870(m) iff m is a prime power (A000961).
%H A079866 David W. Wilson, <a href="/A079866/b079866.txt">Table of n, a(n) for n = 1..10000</a>
%p A079866 A079866 := proc(n)
%p A079866     root[numtheory[bigomega](n)](n) ;
%p A079866     floor(%) ;
%p A079866 end proc:
%p A079866 seq(A079866(n),n=1..97) ; # _R. J. Mathar_, Sep 07 2016
%t A079866 Join[{1}, Table[Floor[n^(1/PrimeOmega[n])], {n, 2, 20}]] (* _G. C. Greubel_, Sep 16 2016 *)
%o A079866 (PARI) a(n) = if (n==1, 1, sqrtnint(n, bigomega(n))); \\ _Michel Marcus_, Sep 09 2016
%Y A079866 A079867(n) = a(n)^A001222(n).
%Y A079866 Cf. A079747, A358890.
%K A079866 nonn
%O A079866 1,2
%A A079866 _Reinhard Zumkeller_, Jan 13 2003