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

Author

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

Keywords

• nonn
• easy
• nice

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

Examples

			36 is the unique number k with k/d(k)=4.
		

Links

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

Crossrefs

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

Programs

Haskell

a051278 n = a051278_list !! (n-1)
a051278_list = filter ((== 1) . a051521) [1..]
-- Reinhard Zumkeller, Dec 28 2011

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 *)