A087134 Smallest number having exactly n divisors that are not greater than the number's greatest prime factor.

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

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 * A370494 A036689 A355390

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