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A305891 Filter sequence combining 2-adic valuation (A007814) and the prime signature (A046523) of n.

%I A305891 #7 Jun 14 2018 20:26:31
%S A305891 1,2,3,4,3,5,3,6,7,5,3,8,3,5,9,10,3,11,3,8,9,5,3,12,7,5,13,8,3,14,3,
%T A305891 15,9,5,9,16,3,5,9,12,3,14,3,8,17,5,3,18,7,11,9,8,3,19,9,12,9,5,3,20,
%U A305891 3,5,17,21,9,14,3,8,9,14,3,22,3,5,17,8,9,14,3,18,23,5,3,20,9,5,9,12,3,24,9,8,9,5,9,25,3,11,17,16,3,14,3,12,26,5,3,27,3
%N A305891 Filter sequence combining 2-adic valuation (A007814) and the prime signature (A046523) of n.
%C A305891 Restricted growth sequence transform of A286161, of the ordered pair [A007814(n), A046523(n)].
%C A305891 For all i, j: a(i) = a(j) => A291761(i) = A291761(j).
%H A305891 Antti Karttunen, <a href="/A305891/b305891.txt">Table of n, a(n) for n = 1..65537</a>
%o A305891 (PARI)
%o A305891 up_to = 65537;
%o A305891 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 A305891 A007814(n) = valuation(n,2);
%o A305891 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
%o A305891 Aux305891(n) = [A007814(n), A046523(n)];
%o A305891 v305891 = rgs_transform(vector(up_to,n,Aux305891(n)));
%o A305891 A305891(n) = v305891[n];
%Y A305891 Cf. A286161, A291761, A305801.
%Y A305891 Cf. also A305893.
%K A305891 nonn
%O A305891 1,2
%A A305891 _Antti Karttunen_, Jun 14 2018