68 lines
1.9 KiB
Text
68 lines
1.9 KiB
Text
const SPHENIC_NUMBERS = Set{Int64}()
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const NOT_SPHENIC_NUMBERS = Set{Int64}()
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function issphenic(n::Int64)
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n in SPHENIC_NUMBERS && return true
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n in NOT_SPHENIC_NUMBERS && return false
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nin = n
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sqn = isqrt(nin)
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npfactors = 0
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isrepeat = false
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i = 2
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while n > 1 && !(npfactors == 0 && i >= sqn)
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if n % i == 0
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npfactors += 1
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if isrepeat || npfactors > 3
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push!(NOT_SPHENIC_NUMBERS, nin)
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return false
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end
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isrepeat = true
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n ÷= i
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continue
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end
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i += 1
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isrepeat = false
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end
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if npfactors < 3
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push!(NOT_SPHENIC_NUMBERS, nin)
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return false
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end
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push!(SPHENIC_NUMBERS, nin)
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return true
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end
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issphenictriple(n::Integer) = issphenic(n) && issphenic(n+1) && issphenic(n+2)
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printlntriple(n::Integer) = println("($(n), $(n+1), $(n+2))")
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shenums = filter(issphenic, 2:1_000_000)
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shetrip = filter(issphenictriple, 2:1_000_000)
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# 1. All sphenic numbers less than 1,000.
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println("Sphenic numbers less than 1,000:")
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less1000 = filter(<(1000), shenums)
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foreach(println, Iterators.partition(less1000, 15))
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# 2. All sphenic triplets less than 10,000.
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println("Sphenic triplets less than 10,000:")
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less10000 = filter(<(10_000 - 6), shetrip)
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foreach(printlntriple, less10000)
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# 3. How many sphenic numbers are there less than 1 million?
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println("Number of sphenic numbers that are less than 1 million: ", length(shenums))
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# 4. How many sphenic triplets are there less than 1 million?
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println("Number of sphenic triplets that are less than 1 million: ", length(shetrip))
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# 5. What is the 200,000th sphenic number and its 3 prime factors?
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println("The 200,000th sphenic number is: ", shenums[200_000])
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# 6. What is the 5,000th sphenic triplet?
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print("The 5,000h sphenic triplet is: ")
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printlntriple(shetrip[5_000])
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