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.

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

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

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

Cf. A033879, A019565, A289813, A295882, A296072, A296073.

Cf. also A293221.

Sequence in context: A344226 A305792 A317942 * A319342 A318834 A353564

Adjacent sequences: A296068 A296069 A296070 * A296072 A296073 A296074

Keyword

nonn

Author

Antti Karttunen, Dec 04 2017

Status

approved