A275465 a(n) = f^(n/f), where f is the smallest prime factor of n.

2, 3, 4, 5, 8, 7, 16, 27, 32, 11, 64, 13, 128, 243, 256, 17, 512, 19, 1024, 2187, 2048, 23, 4096, 3125, 8192, 19683, 16384, 29, 32768, 31, 65536, 177147, 131072, 78125, 262144, 37, 524288, 1594323, 1048576, 41, 2097152, 43, 4194304, 14348907, 8388608, 47, 16777216

Offset: 2

Author

Tyler Skywalker, Jul 28 2016

Keywords

• nonn
• easy

Examples

			For n = 12 = 2^2*3, the smallest prime factor of n is f = 2, so a(12) = f^(n/f) = 2^(12/2) = 2^6 = 64. - _Michael B. Porter_, Jul 31 2016
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 2..1000

Crossrefs

Cf. A020639, A032742.

Programs

Maple

a:= n-> (f-> f^(n/f))(min(numtheory[factorset](n))):
seq(a(n), n=2..50);  # Alois P. Heinz, Dec 11 2017

Mathematica

a[n_] := With[{f = FactorInteger[n][[1, 1]]}, f^(n/f)]; ; Array[a,50,2] (* JungHwan Min, Jul 29 2016 *)(* amended by Harvey P. Dale, Aug 12 2021 *)

PARI

a(n) = my(f=factor(n)[1, 1]); f^(n/f) \\ Felix Fröhlich, Jul 30 2016

Python

from _future_ import division
from sympy import primefactors
def A275465(n):
    p = min(primefactors(n))
    return p**(n//p) # Chai Wah Wu, Jul 29 2016

Formula

a(p) = p, a(p^2) = p^p and a(p^m) = p^(p^(m-1)) for prime p. - Chai Wah Wu, Jul 29 2016

a(n) = A020639(n)^(n/A020639(n)). - Felix Fröhlich, Jul 30 2016

a(n) = A020639(n)^A032742(n). - Chai Wah Wu, Jul 30 2016

Extensions

More terms from Chai Wah Wu, Jul 30 2016