1,3

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 less divisors and all c(k) with k < n have less distinct factors than c(n). (tau(n) and littleomega(c(n)) increase simultaneously to a new record.)

For example a(24)=9979200,

p(24) = 23768741896345550770650537601358310 and

c(24) = 237193029132011520250475844831474847152000.

Every other number n < c(24) has less then tau(c(24))=905969664

divisors and c(1),...,c(23) have less then 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.

Cf. A002182, A161812

Sequence in context: A036045 A100538 A135139 this_sequence A062177 A129643 A096421

Adjacent sequences: A161891 A161892 A161893 this_sequence A161895 A161896 A161897

easy,nonn

Peter Luschny (peter(AT)luschny.de), Jun 21 2009