OFFSET
1,1
COMMENTS
Theorem: There are infinitely many n-th power refactorable numbers for any given value of n > 1.
For proof see Alkan link.
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, ...
Primes p such that a(p-1) is not equal to p are 41, 313, 563, 1013, 1201, 1823, ....
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Altug Alkan, Proof of Theorem
S. Colton, Refactorable Numbers - A Machine Invention, J. Integer Sequences, Vol. 2, 1999.
Joshua Zelinsky, Tau Numbers: A Partial Proof of a Conjecture and Other Results , Journal of Integer Sequences, Vol. 5 (2002), Article 02.2.8
EXAMPLE
a(4) = 5 because 625 = 5^4 is the least fourth power refactorable number that is greater than 1.
PROG
(PARI) isA033950(n) = n % numdiv(n) == 0;
a(n) = my(k=2); while (!isA033950 (k^n), k++); k;
CROSSREFS
KEYWORD
nonn
AUTHOR
Altug Alkan, Jan 22 2017
STATUS
approved