A118224 Smallest number having at least 2*n divisors.

2, 6, 12, 24, 48, 60, 120, 120, 180, 240, 360, 360, 720, 720, 720, 840, 1260, 1260, 1680, 1680, 2520, 2520, 2520, 2520, 5040, 5040, 5040, 5040, 5040, 5040, 7560, 7560, 10080, 10080, 10080, 10080, 15120, 15120, 15120, 15120, 20160, 20160, 25200, 25200, 25200

Offset: 1

Author

Reinhard Zumkeller, Apr 16 2006

Keywords

• nonn

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A086921, A003680 (exactly 2n).

Programs

Mathematica

s={};Do[i=1;Until[DivisorSigma[0,i]>=2n,i++];AppendTo[s,i],{n,45}];s (* James C. McMahon, Sep 24 2024 *)

Python

from sympy import divisors
def a(n):
  m = 4*n - 2
  while len(divisors(m)) < 2*n: m += 1
  return m
print([a(n) for n in range(1, 46)]) # Michael S. Branicky, Feb 06 2021

Formula

A000005(a(n)) >= 2*n;

a(n) = A061799(2*n).

a(n) <= A003680(n). - Michael S. Branicky, Feb 06 2021