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#lang racket
;;; Задача 1
(define (smallest-prime n)
(cond [(= (remainder n 2) 0) 2]
[(= (remainder n 3) 0) 3]
[else (define (find-prime-iter n i maxd)
(cond [(> (sub1 i) maxd) n]
[(= (remainder n (sub1 i)) 0) (sub1 i)]
[(= (remainder n (add1 i)) 0) (add1 i)]
[else (find-prime-iter n (+ i 6) maxd)]))
(find-prime-iter n 6 (sqrt n))]))
(define (sum-prime-divisors n)
(define smallest-prime-of-n (smallest-prime n))
(if (= n 1)
0
(+ smallest-prime-of-n (sum-prime-divisors (quotient n smallest-prime-of-n)))))
;;; Задача 2
(define (pow x n)
(if (= n 0)
1
(* x (pow x (sub1 n)))))
;;; Задача 3
(define (count-occurences d n)
(cond [(= n 0) 0]
[(= (remainder n 10) d)
(add1 (count-occurences d (quotient n 10)))]
[else (count-occurences d (quotient n 10))]))
;;; Задача 4
(define (ascending? n)
(cond [(= n 0) #t]
[(< (remainder n 10) (remainder (quotient n 10) 10)) #f]
[else (ascending? (quotient n 10))]))
;;; Задача 5
(define (smallest-divisor n bigger-than)
(define (calc-iter i)
(if (= (remainder n i) 0)
i
(calc-iter (add1 i))))
(calc-iter (add1 bigger-than)))
(define (perfect-number? n)
(define (calc-iter current-divisor current-sum)
(cond [(= current-divisor n) #f]
[(= current-sum n) #t]
[else (define divisor (smallest-divisor n current-divisor))
(calc-iter divisor (+ current-sum divisor))]))
(calc-iter 1 1))
;;; Задача 6
(define (calc-sum x n)
(define (calc-iter i prev-powd sum)
(define curr-powd (* prev-powd x))
(if (= i n)
sum
(calc-iter (add1 i) curr-powd (+ sum curr-powd))))
(calc-iter 0 1 1))
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