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A281495 Least k > 1 such that k^n is a refactorable number.

%I A281495 #13 Jan 24 2017 01:32:55
%S A281495 2,3,2,5,6,7,2,3,10,11,6,13,9,15,2,17,6,19,10,21,8,23,6,5,26,3,14,29,
%T A281495 30,31,2,33,34,35,6,37,38,39,10,9,42,43,22,15,46,47,6,7,10,51,26,53,6,
%U A281495 55,14,57,58,59,30,61,62,21,2,65,66,67,34,69,70,71,6,73,74,15,38,77,78,79
%N A281495 Least k > 1 such that k^n is a refactorable number.
%C A281495 Theorem: There are infinitely many n-th power refactorable numbers for any given value of n > 1.
%C A281495 For proof see Alkan link.
%C A281495 Numbers n such that a(n) is not equal to A007947(n+1) are 13, 21, 40, 85, 121, 171, 182, 208, 312, 341, 364, 514, 562, 585, 661, 665, 781, ...
%C A281495 Primes p such that a(p-1) is not equal to p are 41, 313, 563, 1013, 1201, 1823, ....
%H A281495 Charles R Greathouse IV, <a href="/A281495/b281495.txt">Table of n, a(n) for n = 1..10000</a>
%H A281495 Altug Alkan, <a href="/A281495/a281495.txt">Proof of Theorem</a>
%H A281495 S. Colton, <a href="https://cs.uwaterloo.ca/journals/JIS/colton/joisol.html">Refactorable Numbers - A Machine Invention</a>, J. Integer Sequences, Vol. 2, 1999.
%H A281495 Joshua Zelinsky, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL5/Zelinsky/zelinsky9.html">Tau Numbers: A Partial Proof of a Conjecture and Other Results </a>, Journal of Integer Sequences, Vol. 5 (2002), Article 02.2.8
%e A281495 a(4) = 5 because 625 = 5^4 is the least fourth power refactorable number that is greater than 1.
%o A281495 (PARI) isA033950(n) = n % numdiv(n) == 0;
%o A281495 a(n) = my(k=2); while (!isA033950 (k^n), k++); k;
%Y A281495 Cf. A001597, A007947, A033950, A036907, A235524.
%K A281495 nonn
%O A281495 1,1
%A A281495 _Altug Alkan_, Jan 22 2017