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A296071 a(n) = Product_{d|n, d 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.

%I A296071 #12 Dec 04 2017 18:36:40
%S A296071 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,
%T A296071 240,2,1080,2,32,60,56,60,120,2,28,90,576,2,3600,2,400,900,168,2,96,
%U A296071 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
%N 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.
%C A296071 Used as a part of filter A296073.
%H A296071 Antti Karttunen, <a href="/A296071/b296071.txt">Table of n, a(n) for n = 1..16384</a>
%F A296071 a(n) = Product_{d|n, d<n} A019565(A289813(A295882(d))).
%o A296071 (PARI)
%o A296071 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_
%o A296071 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))));
%o A296071 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))));
%o A296071 A289813(n) = { my (d=digits(n, 3)); from digits(vector(#d, i, if (d[i]==1, 1, 0)), 2); } \\ From _Rémy Sigrist_
%o A296071 A295882(n) = { my(x = (2*n)-sigma(n)); if(x >= 0,A117967(x),A117968(-x)); };
%o A296071 A296071(n) = { my(m=1); fordiv(n,d,if(d < n,m *= A019565(A289813(A295882(d))))); m; };
%o A296071 (Scheme)
%o A296071 (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))))))
%o A296071 (define (proper-divisors n) (reverse (cdr (reverse (divisors n)))))
%o A296071 (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)))))
%Y A296071 Cf. A033879, A019565, A289813, A295882, A296072, A296073.
%Y A296071 Cf. also A293221.
%K A296071 nonn
%O A296071 1,2
%A A296071 _Antti Karttunen_, Dec 04 2017