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A305790 Filter-sequence combining prime signature of n (A046523) and similar signature obtained when (0,1)-polynomial encoded in the binary expansion of n is factored over Q (A304751).

%I A305790 #7 Jun 10 2018 21:15:13
%S A305790 1,2,2,3,2,4,2,5,6,4,2,7,2,4,4,8,2,9,2,7,4,4,2,10,11,4,12,7,2,13,2,14,
%T A305790 4,4,4,15,2,4,4,10,2,13,2,7,9,4,2,16,6,17,4,7,2,18,19,10,4,4,2,20,2,4,
%U A305790 9,21,4,13,2,7,19,13,2,22,2,4,9,7,19,13,2,16,23,4,2,20,4,4,19,10,2,24,19,7,4,4,4,25,2,9,7,26,2,13,2,10,13
%N A305790 Filter-sequence combining prime signature of n (A046523) and similar signature obtained when (0,1)-polynomial encoded in the binary expansion of n is factored over Q (A304751).
%C A305790 Restricted growth sequence transform of ordered pair [A046523(n), A304751(n)].
%C A305790 For all i, j: a(i) = a(j) => A305821(i) = A305821(j).
%H A305790 Antti Karttunen, <a href="/A305790/b305790.txt">Table of n, a(n) for n = 1..65537</a>
%o A305790 (PARI)
%o A305790 up_to = 65537;
%o A305790 rgs_transform(invec) = { my(occurrences = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(occurrences,invec[i]), my(pp = mapget(occurrences, invec[i])); outvec[i] = outvec[pp] , mapput(occurrences,invec[i],i); outvec[i] = u; u++ )); outvec; };
%o A305790 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
%o A305790 Aux304751(n) = { my(p=0, f=vecsort((factor(Pol(binary(n)))[, 2]), , 4)); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }
%o A305790 Aux305790(n) = [A046523(n), Aux304751(n)];
%o A305790 v305790 = rgs_transform(vector(up_to,n,Aux305790(n)));
%o A305790 A305790(n) = v305790[n];
%Y A305790 Cf. A046523, A101296, A304751, A305821.
%Y A305790 Cf. also A305789.
%K A305790 nonn
%O A305790 1,2
%A A305790 _Antti Karttunen_, Jun 10 2018