

A227068


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


3



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
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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^(n1), 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



