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A229998
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Denominator of d(k)/d(1) + d(k-1)/d(2) + ... + d(k)/d(1), where d(1),d(2),...,d(k) are the unitary divisors of n.
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4
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1, 2, 3, 4, 5, 3, 7, 8, 9, 1, 11, 6, 13, 7, 3, 16, 17, 9, 19, 10, 21, 11, 23, 12, 25, 13, 27, 14, 29, 3, 31, 32, 33, 17, 7, 18, 37, 19, 39, 4, 41, 21, 43, 22, 45, 23, 47, 24, 49, 5, 51, 26, 53, 27, 55, 28, 57, 29, 59, 3, 61, 31, 63, 64, 1, 33, 67, 2, 69, 7
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OFFSET
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1,2
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LINKS
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EXAMPLE
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n = 5 = 5^1 gives 5/1 + 1/5 = 26/5, so a(5) = 5;
n = 6 = (2^1)*(3^1) gives 6/1 + 3/2 + 2/3 + 1/6 = 25/3, so a(6) = 3.
The first 10 sums: 1/1, 5/2, 10/3, 17/4, 26/5, 25/3, 50/7, 65/8, 82/9, 13/1.
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MATHEMATICA
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r[n_] := Select[Divisors[n], GCD[#, n/#] == 1 &]; Table[r[n], {n, 1, 30}]; k[n_] := Length[r[n]]; t[n_] := Table[r[n][[k[n] + 1 - i]]/r[n][[k[1] + i - 1]], {i, 1, k[n]}]; u = Table[Plus @@ t[n], {n, 1, 60}]; Numerator[u] (* A229997 *)
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CROSSREFS
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KEYWORD
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nonn,easy,frac
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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