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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.
1
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.
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
KEYWORD
nonn
AUTHOR
Leroy Quet, May 02 2007
EXTENSIONS
More terms from R. J. Mathar, Oct 15 2007
STATUS
approved