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A300232 Restricted growth sequence transform of A286152, filter combining A051953(n) and A046523(n), cototient and the prime signature of n.

%I A300232 #10 Mar 01 2018 14:53:20
%S A300232 1,2,2,3,2,4,2,5,6,7,2,8,2,9,10,11,2,12,2,12,13,14,2,15,16,17,18,19,2,
%T A300232 20,2,21,22,23,24,25,2,26,27,28,2,29,2,30,31,32,2,33,34,35,36,37,2,38,
%U A300232 27,39,40,41,2,42,2,43,44,45,46,47,2,48,49,47,2,50,2,51,52,53,46,54,2,55,56,57,2,58,40,59,60,61,2,62,36,63,64,65,66,67,2,68,69
%N A300232 Restricted growth sequence transform of A286152, filter combining A051953(n) and A046523(n), cototient and the prime signature of n.
%H A300232 Antti Karttunen, <a href="/A300232/b300232.txt">Table of n, a(n) for n = 1..65537</a>
%e A300232 a(39) = a(55) (= 27) because both are nonsquare semiprimes (3*13 and 5*11), and both have cototient value 15 = 39 - phi(39) = 55 - phi(55).
%o A300232 (PARI)
%o A300232 up_to = 65537;
%o A300232 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 A300232 write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
%o A300232 A051953(n) = (n - eulerphi(n));
%o A300232 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ This function from _Charles R Greathouse IV_, Aug 17 2011
%o A300232 A286152(n) = (2 + ((A051953(n)+A046523(n))^2) - A051953(n) - 3*A046523(n))/2;
%o A300232 write_to_bfile(1,rgs_transform(vector(up_to,n,A286152(n))),"b300232.txt");
%Y A300232 Cf. A046523, A051953, A286152.
%Y A300232 Cf. also A295885, A300223, A300224, A300226, A300229, A300230, A300231, A300233, A300235.
%K A300232 nonn
%O A300232 1,2
%A A300232 _Antti Karttunen_, Mar 01 2018