A079871 a(1)=1 and for n>1: ceiling(n^(1/Omega(n)))^Omega(n), where Omega(n) is the total number of prime factors of n (A001222).

1, 2, 3, 4, 5, 9, 7, 8, 9, 16, 11, 27, 13, 16, 16, 16, 17, 27, 19, 27, 25, 25, 23, 81, 25, 36, 27, 64, 29, 64, 31, 32, 36, 36, 36, 81, 37, 49, 49, 81, 41, 64, 43, 64, 64, 49, 47, 243, 49, 64, 64, 64, 53, 81, 64, 81, 64, 64, 59, 81, 61, 64, 64, 64, 81, 125, 67, 125, 81, 125, 71

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, A079870.

Programs

Mathematica

A079871[n_] := If [n == 1, 1, Ceiling[n^(1/#)]^# & [PrimeOmega[n]]];
Array[A079871, 100] (* Paolo Xausa, Oct 27 2024 *)

PARI

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

Formula

a(n) = A079870(n)^A001222(n).

a(n) >= A079869(n); A020639(n) <= a(n) <= A006530(n);

a(m) = m = A079869(m) iff m is a prime power (A000961).