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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.

%I A340727 #16 Jan 18 2021 18:05:17
%S A340727 12,48,240,1440,8640,60480,604800,5443200,59875200,718502400,
%T A340727 9340531200,124540416000,1743565824000,29640619008000,502146957312000,
%U A340727 8536498274304000,162193467211776000,3406062811447296000,68121256228945920000,1498667637036810240000
%N 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.
%H A340727 James Rayman, <a href="/A340727/b340727.txt">Table of n, a(n) for n = 2..400</a>
%e A340727 a(2) = 12 since 12 = 2*6 = 3*4.
%e A340727 a(4) = 240 since 240 = 2*3*4*10 = 2*3*5*8.
%o A340727 (Python)
%o A340727 from heapq import *
%o A340727 import math
%o A340727 def a(n):
%o A340727     prev, visited, v = 0, set(), list(range(2, n+2))
%o A340727     pq = [(math.factorial(n+1), v)]
%o A340727     while True:
%o A340727         prod, v = heappop(pq)
%o A340727         if tuple(v) in visited: continue
%o A340727         visited.add(tuple(v))
%o A340727         if prev != prod: prev = prod
%o A340727         else: return prod
%o A340727         for i in range(n):
%o A340727             if i == n-1 or v[i] + 1 < v[i+1]:
%o A340727                 u = v[:]
%o A340727                 u[i] += 1
%o A340727                 heappush(pq, (prod // v[i] * u[i], u))
%Y A340727 Cf. A081957.
%K A340727 nonn
%O A340727 2,1
%A A340727 _James Rayman_, Jan 17 2021