A096159 -id:A096159

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A096158

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

+10
2

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, 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, 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

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OFFSET

1,4

COMMENTS

For n>4: a(n)=2 iff (n/2,2+n/2) is twin prime pair, a(2*A001359(n))=2;

a(A096160(n)) > 0.

LINKS

Table of n, a(n) for n=1..102.

EXAMPLE

Proper divisors of n=12 are {1,2,3,4,6}:

[2,3,4,1,6]->(2+3,3+4,4+1,1+6)=(5,7,5,7),

[4,3,2,1,6]->(4+3,3+2,2+1,1+6)=(7,5,3,7),

[6,1,2,3,4]->(6+1,1+2,2+3,3+4)=(7,3,5,7) and

[6,1,4,3,2]->(6+1,1+4,4+3,3+2)=(7,5,7,5): therefore a(12)=4.

CROSSREFS

Cf. A032741, A091954, A000005, A096159.

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Jun 18 2004

STATUS

approved

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