A161894 - OEIS

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A161894

Small factors of some highly composite numbers.

1, 1, 2, 4, 12, 24, 72, 72, 288, 1440, 1440, 10080, 10080, 10080, 30240, 30240, 100800, 100800, 907200, 907200, 907200, 6350400, 9979200, 9979200 (list; graph; refs; listen; history; 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 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.)`
	EXAMPLE	`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.`
	CROSSREFS	`Cf. A002182, A161812` `Sequence in context: A036045 A100538 A135139 * A062177 A129643 A200337` `Adjacent sequences: A161891 A161892 A161893 * A161895 A161896 A161897`
	KEYWORD	`easy,nonn`
	AUTHOR	`Peter Luschny (peter(AT)luschny.de), Jun 21 2009`

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Last modified February 16 06:25 EST 2012. Contains 205860 sequences.