%I A153212
%S A153212 2,4,3,8,6,16,5,9,18,32,15,64,54,12,7,128,10
%N A153212 A permutation of the integers >= 2 which is constructed by swapping each 
               prime's index difference (from the previous prime) and the prime's 
               power in the factorization of a number. In order the "index difference" 
               to make sense the we consider the factorization to be sorted with 
               respect to the primes but not the powers they are raised to, that 
               is, first comes the smallest prime and each subsequent prime is larger 
               than the previous disregarding their powers.
%C A153212 For every n it is true that a(a(n)) = n
%F A153212 denote the i-th prime with p(i): p(1)=2, p(2)=3, p(3)=5, p(4)=7, etc. 
               let n = p(a1)^b1 * p(a2)^b2 * ... * p(ak)^bk is the factorization 
               of n where p(i)^j is the i-th prime raised to power j. As mentioned 
               above, we assume that the primes are sorted, i.e. a1 < a2 < a3... 
               < ak. Then a(n) = p(c1)^d1 * p(c2)^d2 * ... * p(ck)^dk where c1 = 
               b1 and c(i) = b(i) + c(i-1) for i > 1 d1 = a1 and d(i) = a(i) - a(i-1) 
               for i > 1
%e A153212 for n = 10 we have 10 = 2^1 * 5^1 = p(1)^1 * p(3)^1 then a(10) = p(1)^1 
               * p(2)^2 = 2^1 * 3^2 = 18 for n = 18 we have 18 = 2^1 * 3^2 = p(1)^1 
               * p(2)^2 then a(18) = p(1)^1 * p(3)^1 = 2^1 * 5^1 = 10
%Y A153212 Sequence in context: A048672 A127301 A122111 this_sequence A124833 A101468 
               A066194
%Y A153212 Adjacent sequences: A153209 A153210 A153211 this_sequence A153213 A153214 
               A153215
%K A153212 nonn
%O A153212 2,1
%A A153212 Luchezar Belev (l_belev(AT)yahoo.com), Dec 20 2008