A051278 - OEIS

%I #26 May 30 2020 00:09:35

%S 4,6,9,10,12,14,15,20,21,22,26,32,33,34,35,36,38,39,42,46,50,51,55,57,

%T 58,60,62,65,66,69,70,74,75,77,78,82,85,86,87,90,91,93,94,95,96,98,

%U 100,102,106,108,110,111,114,115,118,119,122,123,126,128,129,130

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

%C Because d(k) <= 2*sqrt(k), it suffices to check k from 1 to 4*n^2. - _Nathaniel Johnston_, May 04 2011

%C A051521(a(n)) = 1. - _Reinhard Zumkeller_, Dec 28 2011

%H T. D. Noe, <a href="/A051278/b051278.txt">Table of n, a(n) for n=1..1000</a>

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

%p 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);

%t 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 *)

%o (Haskell)

%o a051278 n = a051278_list !! (n-1)

%o a051278_list = filter ((== 1) . a051521) [1..]

%o -- _Reinhard Zumkeller_, Dec 28 2011

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

%K nonn,easy,nice

%O 1,1

%A _N. J. A. Sloane_, _R. K. Guy_