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A051278
Numbers n such that n = k/d(k) has a unique solution, where d(k) = number of divisors of k.
13
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
OFFSET
1,1
COMMENTS
Because d(k) <= 2*sqrt(k), it suffices to check k from 1 to 4*n^2. - Nathaniel Johnston, May 04 2011
A051521(a(n)) = 1. - Reinhard Zumkeller, Dec 28 2011
EXAMPLE
36 is the unique number k with k/d(k)=4.
MAPLE
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);
MATHEMATICA
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 *)
PROG
(Haskell)
a051278 n = a051278_list !! (n-1)
a051278_list = filter ((== 1) . a051521) [1..]
-- Reinhard Zumkeller, Dec 28 2011
CROSSREFS
KEYWORD
nonn,easy,nice
STATUS
approved