cp's OEIS Frontend

A300224 Filter sequence combining A046523(n) and A296078(n), prime signature of n and prime signature of phi(n)+1.

%I A300224 #5 Mar 01 2018 14:45:07
%S A300224 1,2,2,3,2,4,2,5,3,4,2,6,2,4,7,8,2,6,2,9,4,4,2,10,11,4,5,6,2,12,2,13,
%T A300224 14,4,7,15,2,4,7,16,2,17,2,18,9,4,2,19,3,18,14,9,2,16,4,10,4,4,2,20,2,
%U A300224 4,6,21,7,22,2,18,23,12,2,24,2,4,6,6,4,12,2,25,26,4,2,27,14,4,14,16,2,27,4,28,4,4,4,29,2,6,6,15,2,22,2,10,12
%N A300224 Filter sequence combining A046523(n) and A296078(n), prime signature of n and prime signature of phi(n)+1.
%C A300224 Restricted growth sequence transform of P(A046523(n), A296078(n)), where P(a,b) is a two-argument form of A000027 used as a Cantor pairing function N x N -> N.
%H A300224 Antti Karttunen, <a href="/A300224/b300224.txt">Table of n, a(n) for n = 1..65537</a>
%o A300224 (PARI)
%o A300224 up_to = 65537;
%o A300224 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 A300224 write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
%o A300224 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 A300224 A296078(n) = A046523(1+eulerphi(n));
%o A300224 Aux300224(n) = (1/2)*(2 + ((A296078(n)+A046523(n))^2) - A296078(n) - 3*A046523(n));
%o A300224 write_to_bfile(1,rgs_transform(vector(up_to,n,Aux300224(n))),"b300224.txt");
%Y A300224 Cf. A000010, A046523, A296078.
%Y A300224 Cf. also A286160, A296085, A300223, A300225.
%K A300224 nonn
%O A300224 1,2
%A A300224 _Antti Karttunen_, Mar 01 2018