A296072 a(n) = Product_{d|n, d<n} A019565(A289814(A295882(d))); a product obtained from the -1's present in balanced ternary representation of the deficiencies of the proper divisors of n.

1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 3, 2, 1, 1, 12, 1, 2, 6, 1, 1, 12, 1, 1, 12, 3, 1, 12, 1, 1, 2, 15, 3, 216, 1, 5, 2, 6, 1, 6, 1, 2, 36, 5, 1, 180, 3, 10, 30, 1, 1, 1080, 1, 3, 10, 1, 1, 3240, 1, 1, 36, 1, 1, 20, 1, 450, 10, 30, 1, 45360, 1, 1, 30, 75, 3, 10, 1, 60, 360, 1, 1, 540, 15, 105, 2, 2, 1, 3240, 3, 50, 2, 35, 5, 2520, 1, 630, 60, 90, 1, 900

Offset

1,6

Comments

Used as a part of filter A296073.

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Formula

a(n) = Product_{d|n, d<n} A019565(A289814(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))));
A289814(n) = { my (d=digits(n, 3)); from digits(vector(#d, i, if (d[i]==2, 1, 0)), 2); } \\ From Rémy Sigrist
A295882(n) = { my(x = (2*n)-sigma(n)); if(x >= 0, A117967(x), A117968(-x)); };
A296072(n) = { my(m=1); fordiv(n, d, if(d < n, m *= A019565(A289814(A295882(d))))); m; };
(Scheme)
(define (A296072 n) (let loop ((m 1) (props (proper-divisors n))) (cond ((null? props) m) (else (loop (* m (A019565 (A289814 (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

Cf. A033879, A019565, A289814, A295882, A296071, A296073.

Cf. also A293222.

Sequence in context: A016014 A067760 A078680 * A326700 A050412 A374382

Adjacent sequences: A296069 A296070 A296071 * A296073 A296074 A296075

Keyword

nonn

Author

Antti Karttunen, Dec 04 2017

Status

approved