A185445 Smallest number having exactly t divisors, where t is the n-th triprime (A014612).

24, 60, 180, 240, 900, 960, 720, 2880, 15360, 3600, 6480, 61440, 14400, 46080, 983040, 25920, 32400, 3932160, 184320, 62914560, 233280, 230400, 2949120, 129600, 414720, 11796480, 4026531840, 921600, 16106127360, 810000, 1658880, 188743680, 1166400, 1030792151040, 14745600, 3732480

Offset: 1

Author

Jonathan Vos Post, Feb 03 2011

Keywords

• nonn
• easy

Comments

This is the 3rd row of an infinite array A[k,n] = smallest number having exactly j divisors where j is the n-th natural number with exactly k prime factors (with multiplicity).

The first row is A061286, the second row is A096932.

Examples

			a(10) is 3600 because the 10th triprime is 45, and the smallest number with exactly 45 factors is 3600 = 2^4 * 3^2 * 5^2.
a(20) is 62914560 because the 10th triprime is 92, and the smallest number with exactly 92 factors is 62914560 = 2^22 * 3 * 5.
		

Crossrefs

Cf. A005179, A014612, A061286, A096932.

Programs

Python

from math import isqrt, prod
from sympy import isprime, primepi, primerange, integer_nthroot, prime, divisors
def A185445(n):
    def mult_factors(n):
        if isprime(n):
            return [(n,)]
        c = []
        for d in divisors(n,generator=True):
            if 1Chai Wah Wu, Aug 17 2024

Formula

a(n) = A005179(A014612(n)).