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A318500 Filter sequence combining A305897 and the parity of n.

%I A318500 #10 Jul 10 2019 01:48:14
%S A318500 1,2,3,4,3,5,3,6,7,8,3,9,3,10,11,12,3,13,3,14,15,16,3,17,7,18,19,20,3,
%T A318500 21,3,22,23,24,11,25,3,26,27,28,3,29,3,30,31,32,3,33,7,34,35,36,3,37,
%U A318500 15,38,39,40,3,41,3,42,43,44,23,45,3,46,47,48,3,49,3,50,51,52,11,53,3,54,55,56,3,57,27,58,59,60,3,61,15,62,63,64,35,65,3,66,67,68,3,69,3
%N A318500 Filter sequence combining A305897 and the parity of n.
%C A318500 Restricted growth sequence transform of ordered pair [A000035(n), A246277(n)], or equally, of ordered pair [A007814(n), A246277(n)].
%C A318500 For all i, j:
%C A318500   A305801(i) = A305801(j) => a(i) = a(j) => A305891(i) = A305891(j) => A291761(i) = A291761(j).
%H A318500 Antti Karttunen, <a href="/A318500/b318500.txt">Table of n, a(n) for n = 1..100000</a>
%o A318500 (PARI)
%o A318500 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 A318500 A246277(n) = if(1==n, 0, my(f = factor(n), k = primepi(f[1,1])-1); for (i=1, #f~, f[i,1] = prime(primepi(f[i,1])-k)); factorback(f)/2);
%o A318500 v318500 = rgs_transform(vector(up_to,n,[(n%2),A246277(n)]));
%o A318500 A318500(n) = v318500[n];
%Y A318500 Cf. A246277, A291761, A305801, A305891, A305897.
%K A318500 nonn
%O A318500 1,2
%A A318500 _Antti Karttunen_, Sep 24 2018