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%I #8 Oct 18 2017 00:56:12
%S 1,2,2,3,2,4,2,5,6,7,2,8,2,9,10,11,2,12,2,13,14,15,2,16,4,17,18,19,2,
%T 20,2,21,22,23,24,25,2,26,27,28,2,29,2,30,31,32,2,33,34,35,12,36,2,37,
%U 38,39,40,41,2,42,2,43,44,45,46,47,2,48,49,50,2,51,2,52,53,54,55,56,2,57,58,59,2,60,61,62,63,64,2,65,66,67,68,69,70,71,2,72
%N Restricted growth sequence transform of A293225, a filter combining two products, the other formed from the 1-digits (A293221) and the other from the 2-digits (A293222) present in the ternary expansions of proper divisors of n.
%C For all i, j: a(i) = a(j) => A001065(i) = A001065(j).
%H Antti Karttunen, <a href="/A293226/b293226.txt">Table of n, a(n) for n = 1..19683</a>
%o (PARI)
%o rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
%o write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
%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 A289813(n) = { my (d=digits(n, 3)); fromdigits(vector(#d, i, if (d[i]==1, 1, 0)), 2); };
%o A289814(n) = { my (d=digits(n, 3)); fromdigits(vector(#d, i, if (d[i]==2, 1, 0)), 2); };
%o A293221(n) = { my(m=1); fordiv(n,d,if(d < n,m *= A019565(A289813(d)))); m; };
%o A293222(n) = { my(m=1); fordiv(n,d,if(d < n,m *= A019565(A289814(d)))); m; };
%o Anot_submitted(n) = (1/2)*(2 + ((A293222(n) + A293221(n))^2) - A293222(n) - 3*A293221(n)); \\ Eq.class-wise equal to A293225.
%o write_to_bfile(1,rgs_transform(vector(19683,n,Anot_submitted(n))),"b293226.txt");
%Y Cf. A001065, A293221, A293222, A293223, A293224, A293225.
%Y Cf. also A290093, A290094, A293215, A293217, A293232.
%K nonn
%O 1,2
%A _Antti Karttunen_, Oct 03 2017
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