A227068 Least number with exactly n divisors less than its square root.

2, 6, 12, 24, 48, 60, 144, 120, 180, 240, 3072, 360, 900, 960, 720, 840, 5184, 1260, 36864, 1680, 2880, 3600, 12582912, 2520, 6480, 61440, 6300, 6720, 805306368, 5040, 14400, 7560, 46080, 983040, 25920, 10080, 32400, 746496, 184320, 15120

Offset

1,1

Comments

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).

A056924(a(n)) = n and A056924(m) <> n for m < a(n). - Reinhard Zumkeller, Jul 12 2013

Least k such that there are exactly n couples of distinct divisors whose product is k. [Paolo P. Lava, May 13 2016]

Links

Table of n, a(n) for n=1..40.

Paul Tek, C program for this sequence

Example

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.

Mathematica

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
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 *)

Prog

(Haskell)
import Data.List (elemIndex); import Data.Maybe (fromJust)
a227068 = (+ 1) . fromJust . (`elemIndex` a056924_list)
-- Reinhard Zumkeller, Jul 12 2013
(C) See links section.

Crossrefs

Cf. A005384, A038549, A056924.

Sequence in context: A294545 A305104 A118224 * A003680 A337257 A051487

Adjacent sequences: A227065 A227066 A227067 * A227069 A227070 A227071

Keyword

nonn

Author

T. D. Noe, Jul 11 2013

Extensions

a(29) from Paul Tek, Jul 13 2013

Status

approved