cp's OEIS Frontend

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.

%I A130041 #8 Apr 09 2014 10:14:39
%S A130041 4,9,6,25,16,49,81,8,625,121,64,169,2401,14641,12,289,729,361,15625,
%T A130041 28561,83521,529,36,10,130321,279841,117649,841,100,961,1771561,
%U A130041 707281,923521,1874161,48,1369,2825761,3418801,196,1681,225,1849,4826809
%N 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.
%C A130041 This sequence is a permutation of the composite positive integers.
%e A130041 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)}.
%e A130041 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:
%e A130041 .....2......3......5......7.....11.....13.....17.....19....
%e A130041 .....4......9.....25.....49....121....169....289....361...
%e A130041 .....6......8.....10.....14.....15.....21.....22.....26...
%e A130041 ....16.....81....625...2401..14641..28561..83521.130321....
%e A130041 ....12.....18.....20.....28.....32.....44.....45.....50....
%e A130041 ....64....729..15625.117649.1771561....
%Y A130041 Cf. A130042.
%K A130041 nonn
%O A130041 2,1
%A A130041 _Leroy Quet_, May 02 2007
%E A130041 More terms from _R. J. Mathar_, Oct 15 2007