A051278 Numbers n such that n = k/d(k) has a unique solution, where d(k) = number of divisors of k.

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

Links

T. D. Noe, Table of n, a(n) for n=1..1000

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

Cf. A033950, A036763, A051279, A051280, A051346.

Sequence in context: A319240 A331051 A325270 * A328028 A366318 A339424

Adjacent sequences: A051275 A051276 A051277 * A051279 A051280 A051281

Keyword

nonn,easy,nice

Author

N. J. A. Sloane, R. K. Guy

Status

approved