A130041 Take the integers >= 2. If n is the m-th positive integer with k positive divisors, then replace it with the m-th positive integer with (k+1) positive divisors.

4, 9, 6, 25, 16, 49, 81, 8, 625, 121, 64, 169, 2401, 14641, 12, 289, 729, 361, 15625, 28561, 83521, 529, 36, 10, 130321, 279841, 117649, 841, 100, 961, 1771561, 707281, 923521, 1874161, 48, 1369, 2825761, 3418801, 196, 1681, 225, 1849, 4826809

Offset

2,1

Comments

This sequence is a permutation of the composite positive integers.

Links

Table of n, a(n) for n=2..44.

Example

The number of positive divisors of the integers >= 2 form the sequence 2,2,3,2,4,2,4,3,4,2,6,2,4,4,5,... The number of positive divisors of the terms of {a(j)} form the sequence: 3,3,4,3,5,3,5,4,5,3,7,3,5,5,6,... The n-th term has 1 more divisor than (n+1) has, for every positive integer n. And those terms with the same number of divisors occur in numerical order within {a(j)}.
Comment from R. J. Mathar, Oct 15 2007: This searches for n in the following table (paraphrasing A119586) and replaces n by the value in the same column, but the next row:
.....2......3......5......7.....11.....13.....17.....19....
.....4......9.....25.....49....121....169....289....361...
.....6......8.....10.....14.....15.....21.....22.....26...
....16.....81....625...2401..14641..28561..83521.130321....
....12.....18.....20.....28.....32.....44.....45.....50....
....64....729..15625.117649.1771561....

Crossrefs

Cf. A130042.

Sequence in context: A016097 A083717 A332451 * A109987 A021672 A278810

Adjacent sequences: A130038 A130039 A130040 * A130042 A130043 A130044

Keyword

nonn

Author

Leroy Quet, May 02 2007

Extensions

More terms from R. J. Mathar, Oct 15 2007

Status

approved