A051279 Numbers n such that n = k/d(k) has exactly 2 solutions, where d(k) = number of divisors of k.

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

Cf. A033950, A036763, A051278, A051280, A051346.

Sequence in context: A039580 A361461 A189296 * A288464 A111199 A359381

Adjacent sequences: A051276 A051277 A051278 * A051280 A051281 A051282

Keyword

nonn,easy,nice

Author

N. J. A. Sloane, R. K. Guy, David W. Wilson

Status

approved