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A051278
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Numbers n such that n = k/d(k) has a unique solution, where d(k) = number of divisors of k.
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13
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4, 6, 9, 10, 12, 14, 15, 20, 21, 22, 26, 32, 33, 34, 35, 36, 38, 39, 42, 46, 50, 51, 55, 57, 58, 60, 62, 65, 66, 69, 70, 74, 75, 77, 78, 82, 85, 86, 87, 90, 91, 93, 94, 95, 96, 98, 100, 102, 106, 108, 110, 111, 114, 115, 118, 119, 122, 123, 126, 128, 129, 130
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OFFSET
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1,1
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COMMENTS
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Because d(k) <= 2*sqrt(k), it suffices to check k from 1 to 4*n^2. - Nathaniel Johnston, May 04 2011
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LINKS
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EXAMPLE
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36 is the unique number k with k/d(k)=4.
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MAPLE
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with(numtheory): A051278 := proc(n) local ct, k: ct:=0: for k from 1 to 4*n^2 do if(n=k/tau(k))then ct:=ct+1: fi: od: if(ct=1)then return n: else return NULL: fi: end: seq(A051278(n), n=1..40);
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MATHEMATICA
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cnt[n_] := Count[Table[n == k/DivisorSigma[0, k], {k, 1, 4*n^2}], True]; Select[Range[130], cnt[#] == 1 &] (* Jean-François Alcover, Oct 22 2012 *)
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PROG
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(Haskell)
a051278 n = a051278_list !! (n-1)
a051278_list = filter ((== 1) . a051521) [1..]
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CROSSREFS
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KEYWORD
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nonn,easy,nice
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AUTHOR
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STATUS
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approved
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