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A172398
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Number of partitions of n into the sum of two refactorable numbers.
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0
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0, 1, 1, 1, 0, 0, 0, 0, 1, 2, 1, 0, 1, 1, 0, 1, 1, 1, 1, 2, 1, 0, 0, 1, 1, 2, 1, 0, 0, 1, 0, 1, 1, 0, 0, 2, 1, 1, 0, 0, 1, 2, 0, 1, 1, 0, 0, 3, 1, 0, 0, 1, 0, 1, 0, 0, 1, 2, 0, 1, 1, 1, 0, 2, 1, 0, 0
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OFFSET
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1,10
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COMMENTS
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A number is refactorable if it is divisible by the number of its divisors. - Wesley Ivan Hurt, Jan 12 2013
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LINKS
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Table of n, a(n) for n=1..67.
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FORMULA
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a(n) = sum(((1+floor(i/d(i)) - ceil(i/d(i))) * (1 + floor((n-i)/d(n-i)) - ceil((n-i)/d(n-i)))), i = 1..floor(n/2)). - Wesley Ivan Hurt, Jan 12 2013
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EXAMPLE
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a(10)=2 because 10=1(refactorable)+9(refactorable)=2(refactorable)+8(refactorable).
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MAPLE
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with(numtheory);
a:=n-> sum( ((1 + floor(i/tau(i)) - ceil(i/tau(i))) * (1 + floor((n-i)/tau(n-i)) - ceil((n-i)/tau(n-i))) ), i=1..floor(n/2));
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CROSSREFS
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Cf. A033950, A129363, A175933.
Sequence in context: A182641 A099200 A093578 * A070107 A044933 A025915
Adjacent sequences: A172395 A172396 A172397 * A172399 A172400 A172401
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KEYWORD
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nonn
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AUTHOR
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Juri-Stepan Gerasimov, Nov 20 2010
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EXTENSIONS
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Corrected by D. S. McNeil, Nov 20 2010
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STATUS
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approved
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