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.

12, 48, 240, 1440, 8640, 60480, 604800, 5443200, 59875200, 718502400, 9340531200, 124540416000, 1743565824000, 29640619008000, 502146957312000, 8536498274304000, 162193467211776000, 3406062811447296000, 68121256228945920000, 1498667637036810240000

Offset

2,1

Links

James Rayman, Table of n, a(n) for n = 2..400

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

Adjacent sequences: A340724 A340725 A340726 * A340728 A340729 A340730

Keyword

nonn

Author

James Rayman, Jan 17 2021

Status

approved