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A305893 Filter sequence combining 3-adic valuation (A007949) and the prime signature (A046523) of n.

%I A305893 #6 Jun 14 2018 20:26:38
%S A305893 1,2,3,4,2,5,2,6,7,8,2,9,2,8,5,10,2,11,2,12,5,8,2,13,4,8,14,12,2,15,2,
%T A305893 16,5,8,8,17,2,8,5,18,2,15,2,12,11,8,2,19,4,12,5,12,2,20,8,18,5,8,2,
%U A305893 21,2,8,11,22,8,15,2,12,5,23,2,24,2,8,9,12,8,15,2,25,26,8,2,21,8,8,5,18,2,27,8,12,5,8,8,28,2,12,11,29,2,15,2,18,15
%N A305893 Filter sequence combining 3-adic valuation (A007949) and the prime signature (A046523) of n.
%C A305893 Restricted growth sequence transform of A286463, of the ordered pair [A007949(n), A046523(n)].
%H A305893 Antti Karttunen, <a href="/A305893/b305893.txt">Table of n, a(n) for n = 1..65537</a>
%o A305893 (PARI)
%o A305893 up_to = 65537;
%o A305893 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 A305893 A007949(n) = valuation(n,3);
%o A305893 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
%o A305893 Aux305893(n) = [A007949(n), A046523(n)];
%o A305893 v305893 = rgs_transform(vector(up_to,n,Aux305893(n)));
%o A305893 A305893(n) = v305893[n];
%Y A305893 Cf. A007949, A046523, A286463, A305900.
%Y A305893 Cf. also A305891.
%K A305893 nonn
%O A305893 1,2
%A A305893 _Antti Karttunen_, Jun 14 2018