OFFSET
1,1
COMMENTS
It is proved in the reference that for every positive integer n the orbit n, f(n), f(f(n)), ... is eventually periodic with period 1 or 2.
Includes all numbers whose prime exponents are distinct primes. If n is in this sequence and k is a squarefree number such that (k,n) = 1, then k*n is in this sequence. - Charlie Neder, May 16 2019
LINKS
Paolo P. Lava, Table of n, a(n) for n = 1..5000
M. Farrokhi, The Prime Exponentiation of an Integer: Problem 11315, Amer. Math. Monthly, 116 (2009), 470.
MAPLE
with(numtheory); P:=proc(q) local a0f, a1, a1f, a2, a2f, a3, a3f, a4, a4f, k, n;
for n from 1 to q do a0:=1; a1:=1; a2:=2; a3:=3; a4:=n;
while not (a1=a3 and a2=a4) do a0f:=ifactors(a4)[2];
a1:=mul(a0f[k][2]^a0f[k][1], k=1..nops(a0f)); a1f:=ifactors(a1)[2];
a2:=mul(a1f[k][2]^a1f[k][1], k=1..nops(a1f)); a2f:=ifactors(a2)[2];
a3:=mul(a2f[k][2]^a2f[k][1], k=1..nops(a2f)); a3f:=ifactors(a3)[2];
a4:=mul(a3f[k][2]^a3f[k][1], k=1..nops(a3f)); od;
if a1<>a2 then print(n); fi; od; end: P(10^6); # Paolo P. Lava, Oct 24 2013
MATHEMATICA
f[n_] := Module[{f = Transpose[FactorInteger[n]]}, Times @@ (f[[2]]^f[[1]])]; Select[Range[300], (x = NestWhileList[f, #, UnsameQ, All]; x[[-2]] != x[[-1]]) &] (* T. D. Noe, Oct 24 2013 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
John W. Layman, Apr 23 2009
STATUS
approved