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A319349 Filter sequence combining parity of n, A003557(n) and A051953(n).

%I A319349 #7 Jan 19 2019 04:15:43
%S A319349 1,2,3,4,3,5,3,6,7,8,3,9,3,10,11,12,3,13,3,14,15,16,3,17,18,19,20,21,
%T A319349 3,22,3,23,24,25,26,27,3,28,29,30,3,31,3,32,33,34,3,35,36,37,38,39,3,
%U A319349 40,29,41,42,31,3,43,3,44,45,46,47,48,3,49,50,48,3,51,3,52,53,54,47,55,3,56,57,58,3,59,42,60,61,62,3,63,38,64,65,66,67,68,3,69,70,71,3
%N A319349 Filter sequence combining parity of n, A003557(n) and A051953(n).
%C A319349 Restricted growth sequence transform of triple [A000035(n), A003557(n), A051953(n)], or equally, of triple [A007814(n), A003557(n), A051953(n)], or equally, of ordered pair [A000035(n), A319348(n)].
%H A319349 Antti Karttunen, <a href="/A319349/b319349.txt">Table of n, a(n) for n = 1..65537</a>
%F A319349 For n >= 3, a(n) = 1 + A319348(n).
%o A319349 (PARI)
%o A319349 up_to = 65537;
%o A319349 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 A319349 A003557(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 2] = f[i, 2]-1); factorback(f); };
%o A319349 A051953(n) = (n-eulerphi(n));
%o A319349 v319349 = rgs_transform(vector(up_to,n,[(n%2),A003557(n),A051953(n)]));
%o A319349 A319349(n) = v319349[n];
%Y A319349 Cf. A000035, A003557, A007814, A051953, A305801, A319348.
%K A319349 nonn
%O A319349 1,2
%A A319349 _Antti Karttunen_, Sep 29 2018