[seqfan] Re: Symmetric Relations and Self-Inverse Permutations

[franktaw at netscape.net]

I just submitted:

%I A159587
%S A159587 
1,3,2,5,4,35,8,7,11,21,9,55,16,15,14,13,19,65,17,33,10,39,25,77,23,45,
%T A159587 
29,51,27,1001,32,31,20,57,6,85,41,63,22,69,37,715,47,75,26,87,43,91,53,
%U A159587 
93,28,95,49,115,12,99,34,111,61,1309,59,117,38,67,18,455,64,123,40,429
%N A159587 a(n) is the smallest number not yet in the sequence with the 
same
number of distinct prime divisors as n, but relatively prime to n.
%C A159587 This is a self-inverse permutation of the positive integers.
....

I'm wondering about the record highs for this sequence.  It appears 
that these occur at values in A060735 (numbers p# * k where p# is the 
primorial function of a prime p, and k < q where q is the next prime > 
p).  Certainly all numbers in A060735 are indices of record highs in 
A159587; it seems certain that they are the only ones, but I don't 
quite see how to prove it.

I did check that these are all the record highs up to 1200.

Franklin T. Adams-Watters