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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 16 18:53 EDT 2021. Contains 343050 sequences. (Running on oeis4.)