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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 (list; graph; refs; listen; history; text; internal format)
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
Sequence in context: A039580 A361461 A189296 * A288464 A111199 A359381
KEYWORD
nonn,easy,nice
AUTHOR
STATUS
approved

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Last modified March 19 06:56 EDT 2024. Contains 370953 sequences. (Running on oeis4.)