PlanetMath (more info)
 Math for the people, by the people. Sponsor PlanetMath
Encyclopedia | Requests | Forums | Docs | Wiki | Random | RSS  
Login
create new user
name:
pass:
forget your password?
Main Menu
Owner confidence rating: High Entry average rating: No information on entry rating
[parent] prime factorizations of some small highly composite numbers (Example)

All highly composite numbers have prime factorizations containing consecutive prime numbers, starting with 2, while the exponents form a sequence in descending order (the number 1 as an exponent is tacit in the following table).

HCN Factorization
4 $2^2$
6 $2 \times 3$
12 $2^2 \times 3$
24 $2^3 \times 3$
36 $2^2 \times 3^2$
48 $2^4 \times 3$
60 $2^2 \times 3 \times 5$
120 $2^3 \times 3 \times 5$
180 $2^2 \times 3^2 \times 5$
240 $2^4 \times 3 \times 5$
360 $2^3 \times 3^2 \times 5$
720 $2^4 \times 3^2 \times 5$
840 $2^3 \times 3 \times 5 \times 7$
1260 $2^2 \times 3^2 \times 5 \times 7$
1680 $2^4 \times 3 \times 5 \times 7$
2520 $2^3 \times 3^2 \times 5 \times 7$
5040 $2^4 \times 3^2 \times 5 \times 7$
7560 $2^3 \times 3^3 \times 5 \times 7$
10080 $2^5 \times 3^2 \times 5 \times 7$
15120 $2^4 \times 3^3 \times 5 \times 7$
20160 $2^6 \times 3^2 \times 5 \times 7$
25200 $2^4 \times 3^2 \times 5^2 \times 7$
27720 $2^3 \times 3^2 \times 5 \times 7 \times 11$
45360 $2^4 \times 3^4 \times 5 \times 7$
50400 $2^5 \times 3^2 \times 5^2 \times 7$
55440 $2^4 \times 3^2 \times 5 \times 7 \times 11$
83160 $2^3 \times 3^3 \times 5 \times 7 \times 11$
110880 $2^5 \times 3^2 \times 5 \times 7 \times 11$
166320 $2^4 \times 3^3 \times 5 \times 7 \times 11$
221760 $2^6 \times 3^2 \times 5 \times 7 \times 11$
277200 $2^4 \times 3^2 \times 5^2 \times 7 \times 11$
332640 $2^5 \times 3^3 \times 5 \times 7 \times 11$
498960 $2^4 \times 3^4 \times 5 \times 7 \times 11$
554400 $2^5 \times 3^2 \times 5^2 \times 7 \times 11$
665280 $2^6 \times 3^3 \times 5 \times 7 \times 11$
720720 $2^4 \times 3^2 \times 5 \times 7 \times 11 \times 13$
1081080 $2^3 \times 3^3 \times 5 \times 7 \times 11 \times 13$
1441440 $2^5 \times 3^2 \times 5 \times 7 \times 11 \times 13$
2162160 $2^4 \times 3^3 \times 5 \times 7 \times 11 \times 13$




"prime factorizations of some small highly composite numbers" is owned by PrimeFan.
(view preamble | get metadata)

View style:


This object's parent.
Log in to rate this entry.
(view current ratings)

Cross-references: number, descending order, sequence, exponents, prime numbers, consecutive, prime factorizations, highly composite numbers

This is version 2 of prime factorizations of some small highly composite numbers, born on 2009-03-18, modified 2009-03-21.
Object id is 11670, canonical name is PrimeFactorizationsOfSomeSmallHighlyCompositeNumber.
Accessed 322 times total.

Classification:
AMS MSC11N56 (Number theory :: Multiplicative number theory :: Rate of growth of arithmetic functions)

Pending Errata and Addenda
None.
Discussion
Style: Expand: Order:
forum policy

No messages.

Interact
post | correct | update request | add example | add (any)