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A085892
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Group the natural numbers such that the product of the n-th group has n prime divisors: (1), (2), (3,4), (5,6,), (7,8,9,10), (11,12,13,14), (15,16,17,18,19,20,21), ... Sequence contains the product of the terms of the groups.
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2
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1, 2, 12, 30, 5040, 24024, 586051200, 5967561600, 33891580800, 5846743244160, 70758332701056000, 1929327666754295808000, 228609915104317824000, 8755238159153560237363200, 5998865771053625032442880000
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OFFSET
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0,2
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COMMENTS
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It appears that it is always possible to achieve exactly n prime factors in the n-th group, but a proof would be nice. - Franklin T. Adams-Watters, Sep 07 2006
Empirically, the n-th group has on the order of C*n members (where C >= 1 may not be a constant, but appears to grow slowly); the numbers in that group are then about C*n^2/2. At the end of the group, every prime less than the group size is already present, so the smallest number with two prime factors that are not already present is on the order of (C*n)^2. There are then two ways it might be possible to skip over a value: the apparent growth trend in C could reverse, so that it becomes less than 1/sqrt(2); or there could be an extraordinarily short group. - Franklin T. Adams-Watters, Sep 07 2006
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LINKS
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EXAMPLE
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a(5) = 24024= 11*12*13*14 and the 5 prime divisors are 2,3,7,11 and 13.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jul 10 2003
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EXTENSIONS
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STATUS
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approved
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