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

franktaw at netscape.net franktaw at netscape.net
Thu Apr 16 23:46:42 CEST 2009

I just submitted:

%I A159587
%S A159587 
%T A159587 
%U A159587 
%N A159587 a(n) is the smallest number not yet in the sequence with the 
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

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