A227068 - OEIS

%I #42 Mar 16 2024 11:21:32

%S 2,6,12,24,48,60,144,120,180,240,3072,360,900,960,720,840,5184,1260,

%T 36864,1680,2880,3600,12582912,2520,6480,61440,6300,6720,805306368,

%U 5040,14400,7560,46080,983040,25920,10080,32400,746496,184320,15120

%N Least number with exactly n divisors less than its square root.

%C This is similar to A038549, which counts divisors of n <= sqrt(n). Note that an upper bound on a(n) is 3*2^(n-1), which is attained at n = 2, 3, 4, 5, 11, 23, and 29 -- the number 4 and the primes in A005384 (Sophie Germain primes, p and 2p+1 are prime).

%C A056924(a(n)) = n and A056924(m) <> n for m < a(n). - _Reinhard Zumkeller_, Jul 12 2013

%H Paul Tek, <a href="/A227068/a227068_1.txt">C program for this sequence</a>

%e The divisors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60. Only 6 of these are < sqrt(60). And 60 is the first such number.

%t nn = 22; t = Table[0, {nn}]; found = 0; n = 0; While[found < nn, n++; c = Length[Select[Divisors[n], # < Sqrt[n] &]]; If[c > 0 && c <= nn && t[[c]] == 0, t[[c]] = n; found++]]; t

%t Map[Function[k, FirstPosition[#, k]], Range@ 22] &@ Table[Count[Divisors@ n, m_ /; m < Sqrt@ n], {n, 10^5}] // Flatten (* _Michael De Vlieger_, May 13 2016, Version 10 *)

%o (Haskell)

%o import Data.List (elemIndex); import Data.Maybe (fromJust)

%o a227068 = (+ 1) . fromJust . (`elemIndex` a056924_list)

%o -- _Reinhard Zumkeller_, Jul 12 2013

%o (C) See links section.

%Y Cf. A005384, A038549, A056924.

%K nonn

%O 1,1

%A _T. D. Noe_, Jul 11 2013

%E a(29) from _Paul Tek_, Jul 13 2013