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%I #15 Jul 10 2021 03:52:32
%S 1,2,2,12,2,36,2,120,6,60,2,5400,2,360,30,25200,2,56700,2,21000,180,
%T 840,2,23814000,10,504,630,50400,2,661500,2,554400,420,132,300,
%U 392931000,2,792,252,242550000,2,24948000,2,2772000,22050,1980,2,605113740000,60,4851000,66,3880800,2,720373500,700,4889808000,396,2772,2,588305025000,2,1848
%N a(n) = Product_{d|n, d<n} A019565(A193231(d)).
%H Antti Karttunen, <a href="/A293231/b293231.txt">Table of n, a(n) for n = 1..1024</a>
%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F a(n) = Product_{d|n, d<n} A019565(A193231(d)).
%F For all n >= 1, A007814(a(n)) = A290090(n).
%F For n = 0..5, a(A001317((2^n)-1)) = A002110((2^n)-1).
%o (PARI)
%o 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 A193231(n) = { my(x='x); subst(lift(Mod(1, 2)*subst(Pol(binary(n), x), x, 1+x)), x, 2) }; \\ This function from _Franklin T. Adams-Watters_
%o A293231(n) = { my(m=1); fordiv(n,d,if(d < n,m *= A019565(A193231(d)))); m; };
%Y Cf. A019565, A193231, A290090, A293214, A293232 (rgs-version of this sequence).
%Y Cf. also A001317, A045544, A053576.
%K nonn,base
%O 1,2
%A _Antti Karttunen_, Oct 03 2017
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