cp's OEIS Frontend

A096158 Number of permutations of proper divisors of n such that the sum of adjacent pairs of divisors is prime.

%I A096158 #4 Mar 30 2012 18:50:44
%S A096158 0,0,0,2,0,2,0,2,0,2,0,4,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,4,0,0,0,2,
%T A096158 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,
%U A096158 0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N A096158 Number of permutations of proper divisors of n such that the sum of adjacent pairs of divisors is prime.
%C A096158 For n>4: a(n)=2 iff (n/2,2+n/2) is twin prime pair, a(2*A001359(n))=2;
%C A096158 a(A096160(n)) > 0.
%e A096158 Proper divisors of n=12 are {1,2,3,4,6}:
%e A096158 [2,3,4,1,6]->(2+3,3+4,4+1,1+6)=(5,7,5,7),
%e A096158 [4,3,2,1,6]->(4+3,3+2,2+1,1+6)=(7,5,3,7),
%e A096158 [6,1,2,3,4]->(6+1,1+2,2+3,3+4)=(7,3,5,7) and
%e A096158 [6,1,4,3,2]->(6+1,1+4,4+3,3+2)=(7,5,7,5): therefore a(12)=4.
%Y A096158 Cf. A032741, A091954, A000005, A096159.
%K A096158 nonn
%O A096158 1,4
%A A096158 _Reinhard Zumkeller_, Jun 18 2004