54 lines
1.4 KiB
Plaintext
54 lines
1.4 KiB
Plaintext
import "./fmt" for Fmt
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import "./math" for Int
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var isSquareFree = Fn.new { |n|
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var i = 2
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while (i * i <= n) {
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if (n%(i*i) == 0) return false
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i = (i > 2) ? i + 2 : i + 1
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}
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return true
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}
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var mu = Fn.new { |n|
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if (n < 1) Fiber.abort("Argument must be a positive integer")
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if (n == 1) return 1
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var sqFree = isSquareFree.call(n)
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var factors = Int.primeFactors(n)
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if (sqFree && factors.count % 2 == 0) return 1
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if (sqFree) return -1
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return 0
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}
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var M = Fn.new { |x| (1..x).reduce { |sum, n| sum + mu.call(n) } }
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System.print("The first 199 Mertens numbers are:")
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for (i in 0..9) {
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for (j in 0..19) {
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if (i == 0 && j == 0) {
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System.write(" ")
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} else {
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System.write("%(Fmt.dm(3, M.call(i*20 + j))) ")
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}
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}
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System.print()
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}
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// use the recurrence relationship for the last 2 parts rather than calling M directly
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var count = 0
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var mertens = M.call(1)
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for (i in 2..1000) {
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mertens = mertens + mu.call(i)
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if (mertens == 0) count = count + 1
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}
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System.print("\nThe Mertens function is zero %(count) times in the range [1, 1000].")
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count = 0
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var prev = M.call(1)
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for (i in 2..1000) {
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var next = prev + mu.call(i)
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if (next == 0 && prev != 0) count = count + 1
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prev = next
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}
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System.print("\nThe Mertens function crosses zero %(count) times in the range [1, 1000].")
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