OFFSET
1,1
EXAMPLE
p*q*r*s = 210 is the 27th term in A014613; the smallest number with 210 divisors is 907200 = 2*2*2*2*2*2*3*3*3*3*5*5*7.
PROG
(Python)
from math import prod, isqrt
from sympy import primepi, primerange, integer_nthroot, isprime, divisors, prime
def A061218(n):
def f(x): return int(n+x-sum(primepi(x//(k*m*r))-c for a, k in enumerate(primerange(integer_nthroot(x, 4)[0]+1)) for b, m in enumerate(primerange(k, integer_nthroot(x//k, 3)[0]+1), a) for c, r in enumerate(primerange(m, isqrt(x//(k*m))+1), b)))
def mult_factors(n):
if isprime(n):
return [(n, )]
c = []
for d in divisors(n, generator=True):
if 1<d<n:
for a in mult_factors(n//d):
c.append(tuple(sorted((d, )+a)))
return list(set(c))
m, k = n, f(n)
while m != k:
m, k = k, f(k)
return min((prod(prime(i)**(j-1) for i, j in enumerate(reversed(d), 1)) for d in mult_factors(m)), default=1) # Chai Wah Wu, Aug 17 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Jun 06 2001
EXTENSIONS
Corrected and extended by Michel Marcus, Sep 05 2017
STATUS
approved