OFFSET
1,3
COMMENTS
Definition: Let p(n) be the product of first n primes (primorial A002110) then c(n)=a(n)*p(n) is the unique number such that every other number smaller than c(n) has fewer divisors and all c(k) with k < n have fewer distinct factors than c(n). (tau(n) and littleomega(c(n)) increase simultaneously to a new record.)
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..1229
EXAMPLE
For example a(24)=9979200,
p(24) = 23768741896345550770650537601358310 and
c(24) = 237193029132011520250475844831474847152000.
Every other number n < c(24) has fewer than tau(c(24))=905969664
divisors and c(1),...,c(23) have fewer than 24 distinct factors.
The sequence of corresponding highly composite numbers starts
2
6
60
840
27720
720720
36756720
698377680
64250746560
9316358251200
288807105787200
74801040398884800
3066842656354276800
131874234223233902400
18594267025475980238400
985496152350226952635200
193814243295544634018256000
11822668841028222675113616000
7129069311140018273093510448000
506163921090941297389639241808000
36949966239638714709443664651984000
20433331330520209234322346552547152000
2665090214966421575848043200353649968000
237193029132011520250475844831474847152000
For n > 1 this sequence is conjectured to be a subsequence of A161812.
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Peter Luschny, Jun 21 2009
EXTENSIONS
More terms from Amiram Eldar, Aug 21 2019
STATUS
approved