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A114591
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A composite analogue of the Moebius function: sum{n>=1} a(n)/n^s = product{c=composites} (1 -1/c^s) = zeta(s) *product{k>=2} (1 -1/k^s).
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1
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1, 0, 0, -1, 0, -1, 0, -1, -1, -1, 0, -1, 0, -1, -1, -1, 0, -1, 0, -1, -1, -1, 0, 0, -1, -1, -1, -1, 0, -1
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OFFSET
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1,1
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COMMENTS
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For n >= 2, sum{k|n} (A050370(n/k)) *a(k) = 0. sum{n>=1} a(n)/n^2 = pi^2/12. a(n) = sum{k|n} (A114592(k)).
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LINKS
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Table of n, a(n) for n=1..30.
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FORMULA
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a(1) = 1; for n>= 2, a(n) = sum, over ways to factor n into any number of distinct composites, of (-1)^(number of composites in a factorization). (See example.)
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EXAMPLE
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24 can be factored into distinct composites as 24 and as 4*6.
So a(24) = (-1)^1 + (-1)^2 = 0, where the 1 exponent is due to the 1 factor of the 24 = 24 factorization and the 2 exponent is due to the 2 factors of the 24 = 4*6 factorization.
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CROSSREFS
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Cf. A050370, A114592.
Sequence in context: A121559 A004641 A100810 * A174889 A005171 A076404
Adjacent sequences: A114588 A114589 A114590 * A114592 A114593 A114594
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KEYWORD
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more,sign
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AUTHOR
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Leroy Quet, Dec 11 2005
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STATUS
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approved
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