; gcd sum
(define (range . args)
(case (length args)
((1) (range 0 (car args) (if (negative? (car args)) -1 1)))
((2) (range (car args) (cadr args) (if (< (car args) (cadr args)) 1 -1)))
((3) (let ((le? (if (negative? (caddr args)) >= <=)))
(let loop ((x(car args)) (xs '()))
(if (le? (cadr args) x)
(reverse xs)
(loop (+ x (caddr args)) (cons x xs))))))
(else (error 'range "unrecognized arguments"))))
(define (fold-right op base xs)
(if (null? xs)
base
(op (car xs) (fold-right op base (cdr xs)))))
(define (sum xs) (fold-right + 0 xs))
(define (factors n)
(let loop ((n n) (f 2) (fs (list)))
(cond ((< n (* f f))
(reverse (cons n fs)))
((zero? (modulo n f))
(loop (/ n f) f (cons f fs)))
(else (loop n (+ f 1) fs)))))
(define (divisors n)
(let ((divs (list 1)))
(do ((fs (factors n) (cdr fs)))
((null? fs) (sort divs <))
(let ((temp (list)))
(do ((ds divs (cdr ds)))
((null? ds)
(set! divs (append divs temp)))
(let ((d (* (car fs) (car ds))))
(when (not (member d divs))
(set! temp (cons d temp)))))))))
(define (sigma x n . args) ; sum of x'th powers of divisors of n
(define (add1 n) (+ n 1))
(define (uniq-c eql? xs)
(if (null? xs) xs
(let loop ((xs (cdr xs)) (prev (car xs)) (k 1) (result '()))
(cond ((null? xs) (reverse (cons (cons prev k) result)))
((eql? (car xs) prev) (loop (cdr xs) prev (+ k 1) result))
(else (loop (cdr xs) (car xs) 1 (cons (cons prev k) result)))))))
(define (prod xs) (apply * xs))
(if (= n 1) 1
(let ((fs (uniq-c = (if (pair? args) (car args) (factors n)))))
(if (zero? x)
(prod (map add1 (map cdr fs)))
(prod (map (lambda (p a)
(/ (- (expt p (* (+ a 1) x)) 1) (- (expt p x) 1)))
(map car fs) (map cdr fs)))))))
(define (tau n) (sigma 0 n))
(define (totient n) ; count of positive integers less than n coprime to it
(if (= n 1) 1
(let loop ((t n) (p 0) (fs (factors n)))
(if (null? fs) t
(let ((f (car fs)))
(loop (if (= f p) t (* t (/ (- f 1) f))) f (cdr fs)))))))
(define (moebius n) ; (-1)^k if n has k factors, or 0 if any factors duplicated
(if (= n 1) 1
(let loop ((m 1) (f 0) (fs (factors n)))
(if (null? fs) m
(if (= f (car fs)) 0
(loop (- m) (car fs) (cdr fs)))))))
(define x (* 17 97))
(define (gcd x y)
(if (zero? y) x
(gcd y (modulo x y))))
(define (gcd-sum n)
(let loop ((k 1) (s 0))
(if (< n k) s
(loop (+ k 1) (+ s (gcd k n))))))
(display (gcd-sum x)) (newline)
(define (gcd-sum n)
(let ((sum 0))
(do ((k 1 (+ k 1))) ((< n k) sum)
(set! sum (+ sum (gcd k n))))))
(display (gcd-sum x)) (newline)
(define (gcd-sum n)
(sum (map (lambda (k) (gcd k n)) (range 1 (+ n 1)))))
(display (gcd-sum x)) (newline)
(define (gcd-sum n)
(fold-right (lambda (k s) (+ s (gcd k n))) 0 (range 1 (+ n 1))))
(display (gcd-sum x)) (newline)
(define (gcd-sum n)
(fold-right
(lambda (d s) (+ s (* d (totient (/ n d)))))
0
(divisors n)))
(display (gcd-sum x)) (newline)
(define (gcd-sum n)
(let ((ds (divisors n)))
(fold-right
(lambda (d s) (+ s (* d (tau d) (moebius (/ n d)))))
0
ds)))
(display (gcd-sum x)) (newline)