cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A161894 Small factors of some highly composite numbers.

Original entry on oeis.org

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
Offset: 1

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Author

Peter Luschny, Jun 21 2009

Keywords

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.)

Examples

			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

Extensions

More terms from Amiram Eldar, Aug 21 2019
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