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A051279
Numbers n such that n = k/d(k) has exactly 2 solutions, where d(k) = number of divisors of k.
13
1, 2, 5, 7, 8, 11, 13, 16, 17, 19, 23, 24, 28, 29, 31, 37, 41, 43, 44, 47, 48, 52, 53, 56, 59, 61, 67, 68, 71, 73, 76, 79, 80, 81, 83, 84, 88, 89, 92, 97, 101, 103, 104, 107, 109, 113, 116, 120, 124, 127, 131, 132, 136, 137, 139, 148, 149, 151, 152, 154, 156
OFFSET
1,2
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)) = 2. - Reinhard Zumkeller, Dec 28 2011
LINKS
Nathaniel Johnston and T. D. Noe, Table of n, a(n) for n = 1..1000 (first 150 terms from Nathaniel Johnston)
EXAMPLE
There are exactly 2 numbers k, 40 and 60, with k/d(k)=5.
MAPLE
with(numtheory): A051279 := 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=2)then return n: else return NULL: fi: end: seq(A051279(n), n=1..40); # Nathaniel Johnston, May 04 2011
MATHEMATICA
A051279 = Reap[Do[ct = 0; For[k = 1, k <= 4*n^2, k++, If[n == k/DivisorSigma[0, k], ct++]]; If[ct == 2, Print[n]; Sow[n]], {n, 1, 160}]][[2, 1]](* Jean-François Alcover, Apr 16 2012, after Nathaniel Johnston *)
PROG
(Haskell)
a051279 n = a051279_list !! (n-1)
a051279_list = filter ((== 2) . a051521) [1..]
-- Reinhard Zumkeller, Dec 28 2011
CROSSREFS
KEYWORD
nonn,easy,nice
STATUS
approved