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%I #8 Oct 04 2017 14:05:19
%S 1,2,2,3,2,4,2,5,6,7,2,8,2,9,10,11,2,12,2,13,14,15,2,16,17,18,19,20,2,
%T 21,2,22,23,24,25,26,2,27,28,29,2,30,2,31,32,33,2,34,7,35,36,37,2,38,
%U 28,39,40,41,2,42,2,43,44,45,46,47,2,48,49,50,2,51,2,52,53,54,55,56,2,57,58,59,2,60,61,62,63,64,2,65,66,67,68,69,70,71,2,72,73
%N Restricted growth sequence transform of A293214, where A293214(n) = Product_{d|n, d<n} A019565(d).
%C For all i, j: a(i) = a(j) => A001065(i) = A001065(j).
%H Antti Karttunen, <a href="/A293215/b293215.txt">Table of n, a(n) for n = 1..16384</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 A293214(n) = { my(m=1); fordiv(n,d,if(d < n,m *= A019565(d))); m; };
%o write_to_bfile(1,rgs_transform(vector(16384,n,A293214(n))),"b293215.txt");
%Y Cf. A001065, A019565, A048675, A293214, A293217 (a variant), A293223, A293224, A293226.
%Y Differs from related A293232 for the first time at n=55, where a(55) = 28, while A293232(55) = 39.
%K nonn
%O 1,2
%A _Antti Karttunen_, Oct 03 2017