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A340727
a(n) is the smallest integer that can be written as a product of n distinct integers > 1 in at least two different ways.
1
12, 48, 240, 1440, 8640, 60480, 604800, 5443200, 59875200, 718502400, 9340531200, 124540416000, 1743565824000, 29640619008000, 502146957312000, 8536498274304000, 162193467211776000, 3406062811447296000, 68121256228945920000, 1498667637036810240000
OFFSET
2,1
LINKS
EXAMPLE
a(2) = 12 since 12 = 2*6 = 3*4.
a(4) = 240 since 240 = 2*3*4*10 = 2*3*5*8.
PROG
(Python)
from heapq import *
import math
def a(n):
prev, visited, v = 0, set(), list(range(2, n+2))
pq = [(math.factorial(n+1), v)]
while True:
prod, v = heappop(pq)
if tuple(v) in visited: continue
visited.add(tuple(v))
if prev != prod: prev = prod
else: return prod
for i in range(n):
if i == n-1 or v[i] + 1 < v[i+1]:
u = v[:]
u[i] += 1
heappush(pq, (prod // v[i] * u[i], u))
CROSSREFS
Cf. A081957.
Sequence in context: A339760 A221908 A242026 * A052601 A003498 A326743
KEYWORD
nonn
AUTHOR
James Rayman, Jan 17 2021
STATUS
approved