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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 (list; graph; refs; listen; history; text; internal format)
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

David A. Corneth, Table of n, a(n) for n = 1..10000

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

Cf. A006530, A025487, A087133, A119311, A119312.

Sequence in context: A087150 A323724 A214307 * A036689 A226326 A139115

Adjacent sequences:  A087131 A087132 A087133 * A087135 A087136 A087137

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

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Last modified October 17 18:58 EDT 2019. Contains 328127 sequences. (Running on oeis4.)