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

2,1

Links

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

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A020639, A032742.

Sequence in context: A086931 A243405 A164339 * A185198 A297338 A297457

Adjacent sequences: A275462 A275463 A275464 * A275466 A275467 A275468

Keyword

nonn,easy

Author

Tyler Skywalker, Jul 28 2016

Extensions

More terms from Chai Wah Wu, Jul 30 2016

Status

approved