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A318890 Filter sequence combining the prime signature of n (A046523) with the prime signature of its conjugated prime factorization (A278221).

%I A318890 #6 Sep 16 2018 21:43:37
%S A318890 1,2,3,4,5,6,7,8,9,10,11,12,13,14,10,15,16,12,17,18,19,20,21,22,23,24,
%T A318890 25,26,27,28,29,30,31,32,14,33,34,35,36,37,38,39,40,41,18,42,43,44,45,
%U A318890 18,46,47,48,22,31,49,50,51,52,53,54,55,56,57,58,59,60,61,62,39,63,64,65,66,18,67,20,68,69,70,71,72,73,74,75,76,77,78,79,53,36,80,81,82,83,84,85,26,86,87,88,89,90,91,39
%N A318890 Filter sequence combining the prime signature of n (A046523) with the prime signature of its conjugated prime factorization (A278221).
%C A318890 Restricted growth sequence transform of A286454.
%C A318890 For all i, j: a(i) = a(j) => A318891(i) = A318891(j).
%H A318890 Antti Karttunen, <a href="/A318890/b318890.txt">Table of n, a(n) for n = 1..65537</a>
%o A318890 (PARI)
%o A318890 up_to = 65537;
%o A318890 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 A318890 A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
%o A318890 A122111(n) = if(1==n,n,prime(bigomega(n))*A122111(A064989(n)));
%o A318890 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
%o A318890 A278221(n) = A046523(A122111(n));
%o A318890 A318890aux(n) = [A046523(n), A278221(n)];
%o A318890 v318890 = rgs_transform(vector(up_to,n,A318890aux(n)));
%o A318890 A318890(n) = v318890[n];
%Y A318890 Cf. A046523, A101296, A278221, A286454, A286621, A318891.
%K A318890 nonn
%O A318890 1,2
%A A318890 _Antti Karttunen_, Sep 16 2018