Data commit

Task/Legendre-prime-counting-function/PicoLisp/legendre-prime-counting-function.l

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+(setq Legendre-Max (** 10 9))
+
+(load "plcommon/eratosthenes.l")  # see task "Sieve of Eratosthenes, 2x3x5x7 wheel version.
+
+# Create an index tree of the first N primes up to √Legendre-Max
+(setq Sieve (sieve (sqrt Legendre-Max)))
+(balance 'Primes (mapcar 'cons (range 1 (length Sieve)) Sieve))
+(de prime (N)  (cdr (lup Primes N)))
+
+(de ϕ (X A)
+   (cache '(NIL) (cons X A)
+      (if (=0 A)
+         X
+         (- (ϕ X (dec A)) (ϕ (/ X (prime A)) (dec A))))))
+
+(de π (N)
+   (if (< N 2)
+      0
+      (let A (π (sqrt N))
+         (+ (ϕ N A) A -1))))
+
+(for N 10
+   (prinl "10\^" (dec N) "^I" (π (** 10 (dec N)))))
+
+(bye)