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Sequence: nth number with exactly n divisors: Difference between revisions
Sequence: nth number with exactly n divisors (view source)
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</pre>
=={{header|Haskell}}==
<lang haskell>import Control.Monad (guard)
import Data.List (find, unfoldr)
import Math.NumberTheory.ArithmeticFunctions (divisorCount)
import Math.NumberTheory.Primes (Prime, nextPrime,
unPrime)
import Math.NumberTheory.Primes.Testing (isPrime)
calc :: Integer -> [(Integer, Integer)]
calc n = do
x <- [1..]
guard (even n || odd n && f x ^ 2 == x)
[(x, divisorCount x)]
where f n = floor (sqrt $ realToFrac n)
havingNthDivisors :: Integer -> [(Integer, Integer)]
havingNthDivisors n = filter ((==n) . snd) $ calc n
nths :: [(Integer, Integer)]
nths = do
n <- [1..30] :: [Integer]
if isPrime n then
pure (n, unPrime (nthPrime (fromIntegral n)) ^ (n - 1))
else
pure (n, f n)
where
f n = fst (havingNthDivisors n !! pred (fromIntegral n))
nthPrime n = toEnum n :: Prime Integer
main :: IO ()
main = mapM_ print nths</lang>
{{out}}
<pre>(1,1)
(2,3)
(3,25)
(4,14)
(5,14641)
(6,44)
(7,24137569)
(8,70)
(9,1089)
(10,405)
(11,819628286980801)
(12,160)
(13,22563490300366186081)
(14,2752)
(15,9801)
(16,462)
(17,21559177407076402401757871041)
(18,1044)
(19,740195513856780056217081017732809)
(20,1520)
(21,141376)
(22,84992)
(23,1658509762573818415340429240403156732495289)
(24,1170)
(25,52200625)
(26,421888)
(27,52900)
(28,9152)
(29,1116713952456127112240969687448211536647543601817400964721)
(30,6768)</pre>
=={{header|Java}}==
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