A061299
Least number whose number of divisors is A007304(n) (the n-th number that is the product of 3 distinct primes).
Original entry on oeis.org
720, 2880, 46080, 25920, 184320, 2949120, 129600, 414720, 11796480, 1658880, 188743680, 3732480, 2073600, 26542080, 12079595520, 14929920, 48318382080, 106168320, 8294400, 3092376453120, 1698693120, 18662400, 238878720
Offset: 1
For n = 5: A007304(5) = 78 = 2*3*13, A005179(78) = 184320 = (2^12)*(3^2)*(5^1) = a(5).
A061234
Smallest number with prime(n)^2 divisors where prime(n) is the n-th prime.
Original entry on oeis.org
6, 36, 1296, 46656, 60466176, 2176782336, 2821109907456, 101559956668416, 131621703842267136, 6140942214464815497216, 221073919720733357899776, 10314424798490535546171949056, 13367494538843734067838845976576
Offset: 1
1296 = 2*2*2*2*3*3*3*3 is the smallest number with 25 divisors.
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).
Original entry on oeis.org
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
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.
-
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
A061236
Smallest number with prime(n)^3 divisors where prime(n) is n-th prime.
Original entry on oeis.org
24, 900, 810000, 729000000, 590490000000000, 531441000000000000, 430467210000000000000000, 387420489000000000000000000, 313810596090000000000000000000000, 228767924549610000000000000000000000000000, 205891132094649000000000000000000000000000000
Offset: 1
If p = 2, then d(128) = d(24) = d(30) = 8 and a(1) = 24 < 30 is the smallest.
If p = 5, then 2^124 > (2^24)*(3^4) > 30^4 = 810000 = a(3).
Showing 1-4 of 4 results.
Comments