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URL: https://oeis.org/A296071

⇱ A296071 - OEIS

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A296071
a(n) = Product_{d|n, d<n} A019565(A289813(A295882(d))); a product obtained from the 1's present in balanced ternary representation of the deficiencies of the proper divisors of n.
4
1, 2, 2, 4, 2, 12, 2, 8, 6, 24, 2, 24, 2, 20, 36, 16, 2, 60, 2, 144, 30, 40, 2, 48, 12, 60, 30, 240, 2, 1080, 2, 32, 60, 56, 60, 120, 2, 28, 90, 576, 2, 3600, 2, 400, 900, 168, 2, 96, 10, 1008, 84, 1200, 2, 420, 120, 480, 42, 56, 2, 4320, 2, 84, 1500, 64, 180, 4200, 2, 784, 252, 90720, 2, 1200, 2, 140, 2520, 784, 100, 75600, 2, 1152, 210, 840, 2
OFFSET
1,2
COMMENTS
Used as a part of filter A296073.
LINKS
FORMULA
a(n) = Product_{d|n, d<n} A019565(A289813(A295882(d))).
PROG
(PARI)
A019565(n) = {my(j, v); factorback(Mat(vector(if(n, #n=vecextract(binary(n), "-1..1")), j, [prime(j), n[j]])~))}; \\ This function from M. F. Hasler
A117967(n) = if(n<=1, n, if(!(n%3), 3*A117967(n/3), if(1==(n%3), 1+3*A117967((n-1)/3), 2+3*A117967((n+1)/3))));
A117968(n) = if(1==n, 2, if(!(n%3), 3*A117968(n/3), if(1==(n%3), 2+3*A117968((n-1)/3), 1+3*A117968((n+1)/3))));
A289813(n) = { my (d=digits(n, 3)); from digits(vector(#d, i, if (d[i]==1, 1, 0)), 2); } \\ From Rémy Sigrist
A295882(n) = { my(x = (2*n)-sigma(n)); if(x >= 0, A117967(x), A117968(-x)); };
A296071(n) = { my(m=1); fordiv(n, d, if(d < n, m *= A019565(A289813(A295882(d))))); m; };
(Scheme)
(define (A296071 n) (let loop ((m 1) (props (proper-divisors n))) (cond ((null? props) m) (else (loop (* m (A019565 (A289813 (A295882 (car props))))) (cdr props))))))
(define (proper-divisors n) (reverse (cdr (reverse (divisors n)))))
(define (divisors n) (let loop ((k n) (divs (list))) (cond ((zero? k) divs) ((zero? (modulo n k)) (loop (- k 1) (cons k divs))) (else (loop (- k 1) divs)))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Dec 04 2017
STATUS
approved