A079868 a(1)=1 and for n>1: round(n^(1/Omega(n))), where Omega(n) is the total number of prime factors of n (A001222).

1, 2, 3, 2, 5, 2, 7, 2, 3, 3, 11, 2, 13, 4, 4, 2, 17, 3, 19, 3, 5, 5, 23, 2, 5, 5, 3, 3, 29, 3, 31, 2, 6, 6, 6, 2, 37, 6, 6, 3, 41, 3, 43, 4, 4, 7, 47, 2, 7, 4, 7, 4, 53, 3, 7, 3, 8, 8, 59, 3, 61, 8, 4, 2, 8, 4, 67, 4, 8, 4, 71, 2, 73, 9, 4, 4, 9, 4, 79, 2, 3, 9, 83, 3, 9, 9, 9, 3, 89, 3, 10, 5, 10, 10

Offset: 1

Author

Reinhard Zumkeller, Jan 13 2003

Keywords

• nonn

Comments

A079866(n)<=a(n)<=A079870(n); A020639(n)<=a(n)<=A006530(n);

a(m)=A079866(m)=A079870(m) iff m is a prime power (A000961).

Crossrefs

Cf. A079869(n)=a(n)^A001222(n), A079881.

Programs

Mathematica

Join[{1},Table[Floor[n^(1/PrimeOmega[n])+1/2],{n,2,100}]] (* Harvey P. Dale, Aug 11 2012 *)