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

Author

Reinhard Zumkeller, Aug 17 2003

Keywords

• nonn

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)

Examples

			a(3) = A119313(1) = 6.
		

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

Crossrefs

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

See A221647 for other sequences giving the smallest number whose n-th divisor satisfies some condition.

Programs

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 *)

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

Extensions

More terms from Reinhard Zumkeller, May 15 2006

More terms from Michel Marcus, Sep 21 2014