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 A162936 Highly composite numbers (A002182) whose following highly composite number is at least 3/2 times greater. 1
 1, 2, 4, 6, 12, 24, 60, 120, 240, 360, 840, 1680, 2520, 5040, 10080, 27720, 55440, 110880, 332640, 720720, 1441440, 4324320, 21621600, 73513440, 367567200, 735134400, 1396755360, 6983776800, 13967553600, 27935107200, 160626866400 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS While it can be proved that the related sequence A162935 is finite, I'm not sure whether this sequence is also finite. LINKS PROG (Other) import Data.Ratio import Data.Set (Set) import qualified Data.Set as Set printList :: (Show a) => [a] -> IO() printList = putStr . concat . map (\x -> show x ++ "\n") isPrime n ..| n >= 2 = all isNotDivisor \$ takeWhile smallEnough primes ..| otherwise = False ..where ....isNotDivisor d = n `mod` d /= 0 ....smallEnough d = d^2 <= n primes = 2 : filter isPrime [ 2 * n + 1 | n <- [1..] ] primeSynthesis = partialSynthesis 1 primes ..where ....partialSynthesis n _ [] = n ....partialSynthesis n (p:ps) (c:cs) = partialSynthesis (n * p^c) ps cs primeAnalysis n ..| n < 1 = undefined ..| n == 1 = [] ..| n > 1 = reverse \$ buildPrimeCounts [0] n ..where ....buildPrimeCounts (c:cs) n ......| n == 1 = (c:cs) ......| n `mod` p == 0 = buildPrimeCounts (c+1 : cs) (n `div` p) ......| otherwise = buildPrimeCounts (0:c:cs) n ......where p = primes !! (length cs) divisorCount n = product \$ map (+1) \$ primeAnalysis n primorialProducts = resFrom 1 ..where ....resFrom n = resBetween n (4*n - 1) ++ resFrom (4*n) ....resBetween start end = Set.toAscList \$ Set.fromList \$ unorderedList ......where ........unorderedList = filter (>= start) (1 : build 0 []) ........build pos exponents ..........| nextNumber <= end = nextNumber : build 0 nextCombination ..........| newPrime = [] ..........| otherwise = build (pos + 1) exponents ..........where ............newPrime = pos >= length exponents ............nextCombination ..............| newPrime = replicate (length exponents + 1) 1 ..............| otherwise = replicate (pos + 1) ((exponents !! pos) + 1) ..............................++ drop (pos + 1) exponents ............nextNumber = primeSynthesis nextCombination filterStrictlyMonotonicDivisorCount = filterRest 0 ..where ....filterRest _ [] = [] ....filterRest lim (num:nums) ......| divisorCount num > lim = num : filterRest (divisorCount num) nums ......| otherwise = filterRest lim nums highlyCompositeNumbers ..= filterStrictlyMonotonicDivisorCount primorialProducts findGaps [] = [] findGaps [_] = [] findGaps (x1:x2:xs) ..| x1 * 3 <= x2 * 2 = (x1, x2) : findGaps (x2:xs) ..| otherwise = findGaps (x2:xs) main = mapM (putStrLn . show . fst) (findGaps highlyCompositeNumbers) CROSSREFS Cf. A002182, A162935 Sequence in context: A058764 A087009 A168263 * A036484 A212654 A093036 Adjacent sequences:  A162933 A162934 A162935 * A162937 A162938 A162939 KEYWORD nonn AUTHOR Jan Behrens (jbe-oeis(AT)magnetkern.de), Jul 17 2009 STATUS approved

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