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a(n) = f^(n/f), where f is the smallest prime factor of n.
1

%I #35 Aug 12 2021 17:53:34

%S 2,3,4,5,8,7,16,27,32,11,64,13,128,243,256,17,512,19,1024,2187,2048,

%T 23,4096,3125,8192,19683,16384,29,32768,31,65536,177147,131072,78125,

%U 262144,37,524288,1594323,1048576,41,2097152,43,4194304,14348907,8388608,47,16777216

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

%H Chai Wah Wu, <a href="/A275465/b275465.txt">Table of n, a(n) for n = 2..1000</a>

%F 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

%F a(n) = A020639(n)^(n/A020639(n)). - _Felix Fröhlich_, Jul 30 2016

%F a(n) = A020639(n)^A032742(n). - _Chai Wah Wu_, Jul 30 2016

%e 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

%p a:= n-> (f-> f^(n/f))(min(numtheory[factorset](n))):

%p seq(a(n), n=2..50); # _Alois P. Heinz_, Dec 11 2017

%t 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 *)

%o (Python)

%o from __future__ import division

%o from sympy import primefactors

%o def A275465(n):

%o p = min(primefactors(n))

%o return p**(n//p) # _Chai Wah Wu_, Jul 29 2016

%o (PARI) a(n) = my(f=factor(n)[1, 1]); f^(n/f) \\ _Felix Fröhlich_, Jul 30 2016

%Y Cf. A020639, A032742.

%K nonn,easy

%O 2,1

%A _Tyler Skywalker_, Jul 28 2016

%E More terms from _Chai Wah Wu_, Jul 30 2016