A172443 Numbers with exactly 64 divisors.

7560, 9240, 10920, 11880, 13440, 14040, 14280, 15960, 16632, 17160, 17280, 18360, 19320, 19656, 20520, 20790, 21000, 21120, 22440, 24024, 24192, 24360, 24570, 24840, 24960, 25080, 25704, 26040, 26520, 27000, 28728, 29568, 29640, 30030, 30360, 30888, 31080

Offset: 1

Author

Harvey P. Dale, Nov 20 2010

Keywords

• nonn
• easy

Comments

The first squarefree term of this sequence is the primorial a(34) = 30030.

Almost all terms of this sequence (in the sense of having relative density 1) are squarefree, that is in our case, the product of six distinct primes = A067885. - Charles R Greathouse IV, Aug 27 2021

Examples

			10920 has 64 divisors.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A067885.

Programs

Mathematica

Select[Range[100000],DivisorSigma[0,#]==64&]

PARI

is(n) = numdiv(n) == 64 \\ David A. Corneth, Aug 27 2021

Python

from sympy import divisor_count
def ok(n): return divisor_count(n) == 64
print(list(filter(ok, range(31100)))) # Michael S. Branicky, Aug 27 2021