cp's OEIS Frontend

A178254 Number of permutations of the proper divisors of n such that no adjacent elements have a common divisor greater than 1.

%I A178254 #4 Mar 30 2012 18:51:06
%S A178254 1,1,1,2,1,6,1,2,2,6,1,4,1,6,6,0,1,4,1,4,6,6,1,0,2,6,2,4,1,36,1,0,6,6,
%T A178254 6,0,1,6,6,0,1,36,1,4,4,6,1,0,2,4,6,4,1,0,6,0,6,6,1,0,1,6,4,0,6,36,1,
%U A178254 4,6,36,1,0,1,6,4,4,6,36,1,0,0,6,1,0,6,6,6,0,1,0,6,4,6,6,6,0,1,4,4,0,1,36,1
%N A178254 Number of permutations of the proper divisors of n such that no adjacent elements have a common divisor greater than 1.
%C A178254 Depends only on prime signature;
%C A178254 range = {0, 1, 2, 4, 6, 36};
%C A178254 a(A033987(n)) = 0; a(A037144(n)) > 0;
%C A178254 a(A008578(n))=1; a(A168363(n))=2; a(A054753(n))=4; a(A006881(n))=6; a(A007304(n))=36.
%H A178254 R. Zumkeller, <a href="/A178254/b178254.txt">Table of n, a(n) for n = 1..10000</a>
%H A178254 R. Zumkeller, <a href="/A178254/a178254.txt">Example: n=42</a>
%e A178254 Proper divisors for n=21 are: 1, 3, and 7:
%e A178254 a(39) = #{[1,3,7], [1,7,3], [3,1,7], [3,7,1], [7,1,3], [7,3,1]} = 6;
%e A178254 proper divisors for n=12 are: 1, 2, 3, 4, and 6:
%e A178254 a(12) = #{[2,3,4,1,6], [4,3,2,1,6], [6,1,2,3,4], [6,1,4,3,2]} = 4;
%e A178254 proper divisors for n=42: 1, 2, 3, 6, 7, 14, and 21:
%e A178254 a(42) = #{[2,21,1,6,7,3,14], [2,21,1,14,3,7,6], [3,14,1,6,7,2,21], [3,14,1,21,2,7,6], [6,1,14,3,7,2,21], [6,1,21,2,7,3,14], ...} = 36, see the appended file for the list of all permutations.
%Y A178254 Cf. A109810.
%K A178254 nonn
%O A178254 1,4
%A A178254 _Reinhard Zumkeller_, May 24 2010