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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.)