A132420 a(n) = the 2n-th positive divisor of n!.

24, 15, 16, 16, 20, 24, 27, 27, 30, 30, 33, 36, 40, 40, 44, 44, 48, 50, 52, 52, 55, 57, 63, 65, 68, 68, 70, 70, 75, 77, 80, 84, 87, 87, 90, 92, 95, 95, 98, 98, 100, 104, 108, 108, 111, 114, 116, 119, 121, 121, 124, 126, 129, 132, 135, 135, 138, 138, 141, 144, 147, 150

Offset

4,1

Links

David A. Corneth, Table of n, a(n) for n = 4..10003

Formula

a(n) = A079210(n, 2*n). - Michel Marcus, Apr 25 2022

Example

The positive divisors of 5! = 120 are 1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120. a(5) is the 10th of these, which is 15.

Mathematica

a = {}; For[n = 4, n < 70, n++, i = 1; c = 0; While[c < 2n, If[Mod[n!, i] == 0, c++ ]; i++ ]; AppendTo[a, i - 1]]; a (* Stefan Steinerberger, Nov 24 2007 *)
Table[Divisors[n!][[2n]], {n, 4, 70}] (* Harvey P. Dale, Apr 24 2022 *)

Prog

(PARI) a(n) = { my(t = 0, nf = n!); for(i = n+1, oo, if(nf % i == 0, t++; if(t == n, return(i)) ) ) } \\ David A. Corneth, Apr 25 2022
(Python)
from math import factorial
def a(n):
    nf, t = factorial(n), 0
    for i in range(n+1, nf+1):
        if nf%i == 0: t += 1
        if t == n: return i
print([a(n) for n in range(4, 66)]) # Michael S. Branicky, Apr 25 2022 after David A. Corneth

Crossrefs

Cf. A000142, A079210.

Sequence in context: A075605 A334219 A118661 * A171907 A109475 A105191

Adjacent sequences: A132417 A132418 A132419 * A132421 A132422 A132423

Keyword

nonn

Author

Leroy Quet, Nov 20 2007

Extensions

Corrected and extended by Stefan Steinerberger, Nov 24 2007

Status

approved