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A051707
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Number of factorizations of (n,n) into pairs (j,k).
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7
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1, 1, 1, 3, 1, 5, 1, 8, 3, 5, 1, 23, 1, 5, 5, 23, 1, 23, 1, 23, 5, 5, 1, 91, 3, 5, 8, 23, 1, 52, 1, 60, 5, 5, 5, 143, 1, 5, 5, 91, 1, 52, 1, 23, 23, 5, 1, 328, 3, 23, 5, 23, 1, 91, 5, 91, 5, 5, 1, 339, 1, 5, 23, 161, 5, 52, 1, 23, 5, 52, 1, 686, 1, 5, 23, 23, 5, 52, 1, 328, 23, 5, 1, 339, 5
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OFFSET
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1,4
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COMMENTS
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Pairs (j,k) must satisfy j>1, k>=1; (a,b)*(x,y)=(a*x,b*y); unit is (1,1).
a(n) depends only on prime signature of n (cf. A025487). So a(24) = a(375) since 24=2^3*3 and 375=3*5^3 both have prime signature (3,1).
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LINKS
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Giovanni Resta, Table of n, a(n) for n = 1..1000
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EXAMPLE
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(6,6)=(2,1)*(3,6)=(2,6)*(3,1)=(2,2)*(3,3)=(2,3)*(3,2), so a(6)=5.
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CROSSREFS
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Cf. A050354, A108461, A108455, A348161 (into at most two pairs).
a(A025487) = A108460.
a(p^k) = A108457(k).
a(A002110) = A108459.
Main diagonal of A108455.
Sequence in context: A050329 A147005 A254577 * A302787 A240535 A262397
Adjacent sequences: A051704 A051705 A051706 * A051708 A051709 A051710
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KEYWORD
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nonn,nice,easy
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AUTHOR
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Yasutoshi Kohmoto
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EXTENSIONS
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Edited by Christian G. Bower, Jun 03 2005
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STATUS
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approved
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