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%I #8 Mar 01 2018 14:53:06
%S 1,2,2,3,2,4,2,5,3,6,2,7,2,6,8,9,2,10,2,11,12,6,2,13,3,6,5,14,2,15,2,
%T 16,8,6,12,17,2,6,12,18,2,15,2,7,10,6,2,19,3,20,8,11,2,21,12,22,12,6,
%U 2,23,2,6,20,24,12,15,2,11,8,25,2,26,2,6,20,7,12,15,2,27,9,6,2,28,12,6,8,29,2,30,31,7,12,6,32,33,2,20,10,17,2,15,2,34,35
%N Restricted growth sequence transform of A286570, combining A009194(n) and A046523(n), i.e., gcd(n,sigma(n)) and the prime signature of n.
%H Antti Karttunen, <a href="/A300230/b300230.txt">Table of n, a(n) for n = 1..65537</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 A009194(n) = gcd(n, sigma(n));
%o A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ This function from A046523
%o A286570(n) = (1/2)*(2 + ((A046523(n)+A009194(n))^2) - A046523(n) - 3*A009194(n));
%o write_to_bfile(1,rgs_transform(vector(65537,n,A286570(n))),"b300230.txt");
%Y Cf. A009194, A046523, A286570.
%Y Cf. also A300223, A300226, A300229, A300231, A300232, A300233, A300235.
%K nonn
%O 1,2
%A _Antti Karttunen_, Mar 01 2018