OFFSET

0,2

COMMENTS

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

EXAMPLE

a(5) = 24024= 11*12*13*14 and the 5 prime divisors are 2,3,7,11 and 13.

CROSSREFS

KEYWORD

nonn

AUTHOR

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jul 10 2003

EXTENSIONS

More terms from Ray Chandler, Sep 13 2003

STATUS

approved