factorizations of n! for 1<n<50


The following table gives the exponent for each of the primes from 2 to 47 in the prime factorizationMathworldPlanetmath of n!. Stripping off the zeroes and ignoring the top row and the leftmost column, this table is A115627 in Sloane’s OEIS.

n 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47
2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0
4 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0
5 3 1 1 0 0 0 0 0 0 0 0 0 0 0 0
6 4 2 1 0 0 0 0 0 0 0 0 0 0 0 0
7 4 2 1 1 0 0 0 0 0 0 0 0 0 0 0
8 7 2 1 1 0 0 0 0 0 0 0 0 0 0 0
9 7 4 1 1 0 0 0 0 0 0 0 0 0 0 0
10 8 4 2 1 0 0 0 0 0 0 0 0 0 0 0
11 8 4 2 1 1 0 0 0 0 0 0 0 0 0 0
12 10 5 2 1 1 0 0 0 0 0 0 0 0 0 0
13 10 5 2 1 1 1 0 0 0 0 0 0 0 0 0
14 11 5 2 2 1 1 0 0 0 0 0 0 0 0 0
15 11 6 3 2 1 1 0 0 0 0 0 0 0 0 0
16 15 6 3 2 1 1 0 0 0 0 0 0 0 0 0
17 15 6 3 2 1 1 1 0 0 0 0 0 0 0 0
18 16 8 3 2 1 1 1 0 0 0 0 0 0 0 0
19 16 8 3 2 1 1 1 1 0 0 0 0 0 0 0
20 18 8 4 2 1 1 1 1 0 0 0 0 0 0 0
21 18 9 4 3 1 1 1 1 0 0 0 0 0 0 0
22 19 9 4 3 2 1 1 1 0 0 0 0 0 0 0
23 19 9 4 3 2 1 1 1 1 0 0 0 0 0 0
24 22 10 4 3 2 1 1 1 1 0 0 0 0 0 0
25 22 10 6 3 2 1 1 1 1 0 0 0 0 0 0
26 23 10 6 3 2 2 1 1 1 0 0 0 0 0 0
27 23 13 6 3 2 2 1 1 1 0 0 0 0 0 0
28 25 13 6 4 2 2 1 1 1 0 0 0 0 0 0
29 25 13 6 4 2 2 1 1 1 1 0 0 0 0 0
30 26 14 7 4 2 2 1 1 1 1 0 0 0 0 0
31 26 14 7 4 2 2 1 1 1 1 1 0 0 0 0
32 31 14 7 4 2 2 1 1 1 1 1 0 0 0 0
33 31 15 7 4 3 2 1 1 1 1 1 0 0 0 0
34 32 15 7 4 3 2 2 1 1 1 1 0 0 0 0
35 32 15 8 5 3 2 2 1 1 1 1 0 0 0 0
36 34 17 8 5 3 2 2 1 1 1 1 0 0 0 0
37 34 17 8 5 3 2 2 1 1 1 1 1 0 0 0
38 35 17 8 5 3 2 2 2 1 1 1 1 0 0 0
39 35 18 8 5 3 3 2 2 1 1 1 1 0 0 0
40 38 18 9 5 3 3 2 2 1 1 1 1 0 0 0
41 38 18 9 5 3 3 2 2 1 1 1 1 1 0 0
42 39 19 9 6 3 3 2 2 1 1 1 1 1 0 0
43 39 19 9 6 3 3 2 2 1 1 1 1 1 1 0
44 41 19 9 6 4 3 2 2 1 1 1 1 1 1 0
45 41 21 10 6 4 3 2 2 1 1 1 1 1 1 0
46 42 21 10 6 4 3 2 2 2 1 1 1 1 1 0
47 42 21 10 6 4 3 2 2 2 1 1 1 1 1 1
48 46 22 10 6 4 3 2 2 2 1 1 1 1 1 1
49 46 22 10 8 4 3 2 2 2 1 1 1 1 1 1
Title factorizations of n! for 1<n<50
Canonical name FactorizationsOfNFor1N50
Date of creation 2013-03-22 18:01:14
Last modified on 2013-03-22 18:01:14
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 4
Author PrimeFan (13766)
Entry type Example
Classification msc 11A51