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A066620
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Number of decompositions of divisors of n into pairwise coprime triples.
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1
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0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 1, 1, 0, 0, 2, 0, 2, 1, 1, 0, 3, 0, 1, 0, 2, 0, 7, 0, 0, 1, 1, 1, 4, 0, 1, 1, 3, 0, 7, 0, 2, 2, 1, 0, 4, 0, 2, 1, 2, 0, 3, 1, 3, 1, 1, 0, 13, 0, 1, 2, 0, 1, 7, 0, 2, 1, 7, 0, 6, 0, 1, 2, 2, 1, 7, 0, 4, 0, 1, 0, 13, 1, 1, 1, 3, 0, 13, 1, 2, 1, 1, 1, 5, 0, 2, 2, 4, 0, 7, 0
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OFFSET
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1,12
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COMMENTS
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a(m) = a(n) if m and n have same factorization structure.
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REFERENCES
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Amarnath Murthy, Decomposition of the divisors of a natural number into pairwise coprime sets, Smarandache Notions Journal, vol. 12, No. 1-2-3, Spring 2001.pp 303-306.
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LINKS
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Table of n, a(n) for n=1..103.
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FORMULA
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In the reference it is shown that if k is a squarefree number with r prime factors and m with (r+1) prime factors then a(m) = 4*a(k) + 2^k - 1.
a(n) = (tau(n^3)-3*tau(n)+2)/6. - Vladeta Jovovic, Nov 27 2004
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EXAMPLE
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a(24) = 3: the divisors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24. The decompositions are (1, 2, 3), (1, 2, 9), (1, 3, 4); a(30) = 7: the triples are (1, 2, 3), (1, 2, 5), (1, 3, 5), (2, 3, 5), (1, 3, 10), (1, 5, 6), (1, 2, 15).
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CROSSREFS
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Cf. A063647, A000005.
Sequence in context: A067742 A214772 A089233 * A219023 A025427 A091586
Adjacent sequences: A066617 A066618 A066619 * A066621 A066622 A066623
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KEYWORD
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nonn,changed
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AUTHOR
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K. B. Subramaniam (kb_subramaniambalu(AT)yahoo.com) and Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Dec 24 2001
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EXTENSIONS
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More terms from Vladeta Jovovic, Apr 03 2003
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STATUS
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approved
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