A079869 a(1)=1 and for n>1: round(n^(1/Omega(n)))^Omega(n), where Omega(n) is the total number of prime factors of n (A001222).

1, 2, 3, 4, 5, 4, 7, 8, 9, 9, 11, 8, 13, 16, 16, 16, 17, 27, 19, 27, 25, 25, 23, 16, 25, 25, 27, 27, 29, 27, 31, 32, 36, 36, 36, 16, 37, 36, 36, 81, 41, 27, 43, 64, 64, 49, 47, 32, 49, 64, 49, 64, 53, 81, 49, 81, 64, 64, 59, 81, 61, 64, 64, 64, 64, 64, 67, 64, 64, 64, 71, 32, 73

Offset

1,2

Comments

A079867(n)<=a(n)<=A079869(n); A020639(n)<=a(n)<=A006530(n);

a(m)=m=A079867(m)=A079871(m) iff m is a prime power (A000961).

Links

Table of n, a(n) for n=1..73.

Mathematica

ron[n_]:=Module[{c=PrimeOmega[n]}, Round[n^(1/c)]^c]; Join[{1}, Array[ ron, 80, 2]] (* Harvey P. Dale, Jun 17 2020 *)

Crossrefs

a(n)=A079868(n)^A001222(n). Cf. A079872, A068794, A068795.

Sequence in context: A273284 A079867 A273290 * A200322 A361479 A075054

Adjacent sequences: A079866 A079867 A079868 * A079870 A079871 A079872

Keyword

nonn

Author

Reinhard Zumkeller, Jan 13 2003

Status

approved