A051279 - OEIS

%I #27 Oct 07 2017 01:16:30

%S 1,2,5,7,8,11,13,16,17,19,23,24,28,29,31,37,41,43,44,47,48,52,53,56,

%T 59,61,67,68,71,73,76,79,80,81,83,84,88,89,92,97,101,103,104,107,109,

%U 113,116,120,124,127,131,132,136,137,139,148,149,151,152,154,156

%N Numbers n such that n = k/d(k) has exactly 2 solutions, 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)) = 2. - _Reinhard Zumkeller_, Dec 28 2011

%H Nathaniel Johnston and T. D. Noe, <a href="/A051279/b051279.txt">Table of n, a(n) for n = 1..1000</a> (first 150 terms from Nathaniel Johnston)

%e There are exactly 2 numbers k, 40 and 60, with k/d(k)=5.

%p 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

%t 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_ *)

%o (Haskell)

%o a051279 n = a051279_list !! (n-1)

%o a051279_list = filter ((== 2) . a051521) [1..]

%o -- _Reinhard Zumkeller_, Dec 28 2011

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

%K nonn,easy,nice

%O 1,2

%A _N. J. A. Sloane_, _R. K. Guy_, _David W. Wilson_