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A208251
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Number of refactorable numbers less than or equal to n.
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3
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1, 2, 2, 2, 2, 2, 2, 3, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11
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OFFSET
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1,2
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COMMENTS
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A number is refactorable if it is divisible by the number of its divisors.
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LINKS
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FORMULA
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a(n) = Sum_{i=1..n} 1 + floor(i/d(i)) - ceiling(i/d(i)), where d(n) is the number of divisors of n.
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EXAMPLE
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a(1) = 1 since 1 is the first refactorable number, a(2) = 2 since there are two refactorable numbers less than or equal to 2, a(3) through a(7) = 2 since the next refactorable number is 8.
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MAPLE
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with(numtheory) a:=n->sum((1 + floor(i/tau(i)) - ceil(i/tau(i))), i=1..n);
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MATHEMATICA
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Accumulate[Table[If[Divisible[n, DivisorSigma[0, n]], 1, 0], {n, 1, 100}]] (* Amiram Eldar, Oct 11 2023 *)
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PROG
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(PARI) a(n) = sum(i=1, n, q = i/numdiv(i); 1+ floor(q) - ceil(q)); \\ Michel Marcus, Sep 10 2018
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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