A061218 Least number whose number of divisors is n-th term from A014613 (numbers of form p*q*r*s, products of exactly 4 primes, counted with multiplicity).

120, 360, 1260, 1680, 6300, 6720, 5040, 44100, 20160, 107520, 25200, 45360, 430080, 100800, 322560, 176400, 6881280, 181440, 226800, 27525120, 1290240, 440401920, 705600, 1632960, 1612800, 20643840, 907200, 2903040, 1587600, 82575360, 28185722880, 6451200, 112742891520

Offset: 1

Author

Labos Elemer, Jun 06 2001

Keywords

• nonn

Examples

			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.
		

Crossrefs

Cf. A000005, A005179, A014613, A061148, A061149, A061299.

Programs

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 1Chai Wah Wu, Aug 17 2024

Formula

a(n) = A005179(A014613(n)).

Extensions

Corrected and extended by Michel Marcus, Sep 05 2017