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May 21, 2022 21:47
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(ns euler.p549-divisibility-of-factorials-v4) | |
(defn to-the-power [factor exp] | |
(reduce * 1 (repeat exp factor))) | |
(defn a-prime-factor-for-all-to | |
([max-n] | |
(loop [pfs (apply vector-of :int (range 0 (inc max-n))) | |
n 2] | |
(if (<= (to-the-power n 2) max-n) | |
(let [new-pfs (if (= n (get pfs n)) | |
(reduce #(assoc %1 %2 n) | |
pfs | |
(range (* n 2) (inc max-n) n)) ; found new prime | |
pfs)] | |
(recur new-pfs (inc n))) | |
pfs)))) | |
(defn prime-factors-of [pre-calculated-pfs x] | |
(loop [to-factorise x | |
factors '()] | |
(let [factor (get pre-calculated-pfs to-factorise)] | |
(if (= to-factorise 1) | |
factors | |
(recur (/ to-factorise factor) (conj factors factor)))))) | |
(defn smallest-m-for-power-of-factor | |
"Find m where m! is divisible by pf ^ power. | |
m! is made up of factors 1..m but we are only interested in those factors that are multiples of pf." | |
[pf power] | |
(loop [m-to-try pf] | |
(let [product-of-multiples-of-pf (apply * (range pf (inc m-to-try) pf))] | |
;instead of seeing if (!m-to-try) is divisible by the pf ^ power, just look at the product of the | |
; multiples of `pf` up to m-to-try. | |
(if (zero? (mod product-of-multiples-of-pf (to-the-power pf power))) | |
m-to-try | |
(recur (+ m-to-try pf)))))) | |
(def smallest-m-for-power-of-factor-memoized (memoize smallest-m-for-power-of-factor)) | |
(defn power-of-pf-less-than-or-equal-to-m | |
[pf m] | |
(last (take-while | |
(fn [power] (>= m (to-the-power pf power))) | |
(range)))) | |
(defn occurances-of-pf-in-product-of-series-1-to-m | |
"only looking at ms that are a multiple of pf" | |
[pf m] | |
(+ (/ m pf) (apply + (range (power-of-pf-less-than-or-equal-to-m pf m))))) | |
(defn smallest-m-for-primes [f-pf-n] | |
(apply max (map (fn [[factor freq]] (smallest-m-for-power-of-factor factor freq)) f-pf-n))) | |
(defn seq-of-smallest-m-till-p [p] | |
(let [pfs (a-prime-factor-for-all-to p)] | |
(->> | |
(range 2 (inc p)) | |
(map (fn [x] (frequencies (prime-factors-of pfs x)))) | |
(map smallest-m-for-primes)))) | |
(defn -main [& args] | |
(doall (map #(let [n-to % | |
p (to-the-power 10 %)] | |
(do (println (str "sum of series to 1e" n-to)) | |
(println (time (apply + (seq-of-smallest-m-till-p p)))))) | |
(range 2 9)))) | |
;(defn -main [& args] | |
; (doall (map #(let [p (x-to-power-n 10 %)] | |
; (do (println "sum of prime factor series to " p) | |
; (println (time (seq-of-smallest-m-till-p p))))) | |
; (range 2 8)))) | |
;(defn -main [& args] | |
; (println (time (apply + (sum-of-smallest-m-till-p (int 1e2)))))) |
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