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