The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

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