

A120332


If n is among earlier terms of sequence, then replace each prime power in the primefactorization of n with the next lower primepower to get a(n). If n is not among earlier terms of sequence, then replace each prime power in the primefactorization of n with the next higher primepower to get a(n).


0



1, 3, 2, 5, 4, 12, 8, 7, 11, 21, 9, 6, 16, 24, 28, 13, 19, 33, 17, 35, 10, 39, 25, 14, 23, 48, 29, 15, 27, 84, 32, 31, 18, 57, 20, 55, 41, 69, 22, 63, 37, 96, 47, 65, 77, 75, 43, 26, 53, 81, 76, 80, 49, 87, 36, 72, 34, 93, 61, 140, 59, 96, 40, 67, 44, 156, 64, 95, 38, 168, 73
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

Sequence is a permutation of the positive integers and is its own inverse permutation.


LINKS

Table of n, a(n) for n=1..71.


EXAMPLE

6 (= 2*3) is not among the first 5 terms of the sequence. So for a(6) we want the prime powers closest to and larger than 2 and 3, which are 3 and 4. So a(6) = 3*4 = 12. Therefore 12 (=2^2 *3) does occur among the first 11 terms of the sequence. So for a(12) we want the product of the prime powers closest to and less than 2^2 and 3, which are 3 and 2. So a(12) = 3*2 = 6.


PROG

(PARI) { a(n) = local(f, r, k, d, j); f=factorint(n); r=1; if(setsearch(S, n), j=1, j=1); for(i=1, matsize(f)[1], k=f[i, 1]^f[i, 2]+j; while(k>1 && !isprime(k) && (!ispower(k, X=X, &d)!isprime(d)), k+=j); r*=k); S=setunion(S, [r]); r } S=Set(); vector(100, n, a(n))  Max Alekseyev, Mar 26 2007


CROSSREFS

Cf. A120635, A120636.
Sequence in context: A054158 A054080 A164379 * A302698 A205401 A095006
Adjacent sequences: A120329 A120330 A120331 * A120333 A120334 A120335


KEYWORD

nonn


AUTHOR

Leroy Quet, Jun 22 2006


EXTENSIONS

More terms from Max Alekseyev, Mar 26 2007


STATUS

approved



