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%I #10 Nov 04 2018 20:32:30
%S 1,2,2,3,2,2,2,3,4,2,2,5,2,2,6,7,2,3,2,6,2,3,2,6,8,2,3,3,2,6,2,3,9,2,
%T 6,10,2,2,11,2,2,3,2,9,11,2,2,3,12,13,9,6,2,3,2,11,2,2,2,2,2,3,2,14,6,
%U 15,2,16,17,11,2,11,2,2,3,2,3,6,2,15,18,5,2,6,9,2,15,2,2,6,3,19,2,3,3,9,2,20,3,21,2,15,2,11,6
%N Filter sequence combining A296078(n) and A296091(n), the prime signatures of phi(n)+1 and sigma(n)-1, with a(1) = 1.
%C Restricted growth sequence transform of P(A296078(n), A296091(n)), where P(a,b) is a two-argument form of A000027 used as a Cantor pairing function N x N -> N.
%H Antti Karttunen, <a href="/A300225/b300225.txt">Table of n, a(n) for n = 1..65537</a>
%o (PARI)
%o up_to = 65537;
%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 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 A296078(n) = A046523(1+eulerphi(n));
%o A296091(n) = if(1==n,n,A046523(sigma(n)-1);)
%o Aux300225(n) = (1/2)*(2 + ((A296078(n)+A296091(n))^2) - A296078(n) - 3*A296091(n));
%o write_to_bfile(1,rgs_transform(vector(up_to,n,Aux300225(n))),"b300225.txt");
%Y Cf. A000010, A000203, A296078, A296091.
%Y Cf. also A296085, A300223, A300224.
%K nonn
%O 1,2
%A _Antti Karttunen_, Mar 01 2018
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