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A087134
Smallest number having exactly n divisors that are not greater than the number's greatest prime factor.
6
1, 2, 6, 20, 42, 84, 156, 312, 684, 1020, 1380, 1860, 3480, 3720, 4920, 7320, 10980, 14640, 16920, 21960, 26280, 34920, 45720, 59640, 69840, 89880, 106680, 125160, 145320, 177240, 213360, 244440, 269640, 354480, 320040, 375480, 435960, 456120, 531720, 647640
OFFSET
1,2
COMMENTS
A087133(a(n))=n.
Also smallest number such that the n-th divisor is prime. - Reinhard Zumkeller, May 15 2006
From David A. Corneth, Jan 22 2019: (Start)
For the first 10000 terms except 1, a(n) is of the form A025487(k) * p where p is the smallest prime larger than the n-th divisor and, if the (n+1)-th divisor exists, less than that divisor.
This sequence isn't a sequence of indices of records to A087133 as it's not monotonically increasing; 354480 = a(34) > a(35) = 320040. (End)
LINKS
Eric Weisstein's World of Mathematics, Divisor Function
Eric Weisstein's World of Mathematics, Greatest Prime Factor
EXAMPLE
a(3) = A119313(1) = 6.
MATHEMATICA
With[{s = Array[Function[{d, p}, LengthWhile[d, # < p &]] @@ {#, SelectFirst[Reverse@ #, PrimeQ]} &@ Divisors@ # &, 10^6]}, Array[FirstPosition[s, #][[1]] &, Max@ s + 1, 0]] (* Michael De Vlieger, Jan 23 2019 *)
PROG
(PARI) a087133(n) = if (n==1, 1, my(f = factor(n), gpf = f[#f~, 1]); sumdiv(n, d, d <= gpf));
a(n) = my(k = 1); while (a087133(k) != n, k++); k; \\ Michel Marcus, Sep 21 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Aug 17 2003
EXTENSIONS
More terms from Reinhard Zumkeller, May 15 2006
More terms from Michel Marcus, Sep 21 2014
STATUS
approved