A120332 If n is among earlier terms of sequence, then replace each prime power in the prime-factorization of n with the next lower prime-power to get a(n). If n is not among earlier terms of sequence, then replace each prime power in the prime-factorization of n with the next higher prime-power to get a(n).

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

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: A054080 A356067 A164379 * A302698 A205401 A366264

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