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A161894 Small factors of some highly composite numbers. 1
1, 1, 2, 4, 12, 24, 72, 72, 288, 1440, 1440, 10080, 10080, 10080, 30240, 30240, 100800, 100800, 907200, 907200, 907200, 6350400, 9979200, 9979200, 69854400, 69854400, 69854400, 129729600, 129729600, 259459200, 1210809600, 1816214400, 3632428800, 3632428800 (list; graph; refs; listen; history; text; internal format)
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

Cf. A002182, A161812.

Sequence in context: A100538 A303794 A135139 * A062177 A129643 A332644

Adjacent sequences:  A161891 A161892 A161893 * A161895 A161896 A161897

KEYWORD

easy,nonn

AUTHOR

Peter Luschny, Jun 21 2009

EXTENSIONS

More terms from Amiram Eldar, Aug 21 2019

STATUS

approved

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Last modified July 30 23:12 EDT 2021. Contains 346365 sequences. (Running on oeis4.)