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A296072 a(n) = Product_{d|n, d 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.

%I A296072 #12 Dec 04 2017 18:36:49
%S A296072 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,
%T A296072 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,
%U A296072 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
%N 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.
%C A296072 Used as a part of filter A296073.
%H A296072 Antti Karttunen, <a href="/A296072/b296072.txt">Table of n, a(n) for n = 1..16384</a>
%F A296072 a(n) = Product_{d|n, d<n} A019565(A289814(A295882(d))).
%o A296072 (PARI)
%o A296072 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 A296072 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 A296072 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 A296072 A289814(n) = { my (d=digits(n, 3)); from digits(vector(#d, i, if (d[i]==2, 1, 0)), 2); } \\ From _Rémy Sigrist_
%o A296072 A295882(n) = { my(x = (2*n)-sigma(n)); if(x >= 0,A117967(x),A117968(-x)); };
%o A296072 A296072(n) = { my(m=1); fordiv(n,d,if(d < n,m *= A019565(A289814(A295882(d))))); m; };
%o A296072 (Scheme)
%o A296072 (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))))))
%o A296072 (define (proper-divisors n) (reverse (cdr (reverse (divisors n)))))
%o A296072 (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 A296072 Cf. A033879, A019565, A289814, A295882, A296071, A296073.
%Y A296072 Cf. also A293222.
%K A296072 nonn
%O A296072 1,6
%A A296072 _Antti Karttunen_, Dec 04 2017