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).

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, 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, 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

Offset: 1

Author

Reinhard Zumkeller, Jan 13 2003

Keywords

• nonn

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001222, A006530, A020639, A068794, A068795, A079869, A079871.

Programs

Mathematica

A079870[n_] := If [n == 1, 1, Ceiling[n^(1/PrimeOmega[n])]];
Array[A079870, 100] (* Paolo Xausa, Oct 28 2024 *)

PARI

a(n) = if (n==1, 1, ceil(n^(1/bigomega(n)))); \\ Michel Marcus, May 31 2016

Formula

A079871(n) = a(n)^A001222(n).

a(n) >= A079868(n); A020639(n) <= a(n) <= A006530(n);

a(m) = A079868(m) iff m is a prime power (A000961).