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A304751 Filter sequence: Restricted growth sequence transform of function that gives the least natural number with the same prime signature that (0,1)-polynomial encoded in the binary expansion of n has when it is factored over Q.

%I A304751 #7 Jun 08 2018 13:52:21
%S A304751 1,2,2,3,2,4,2,5,4,4,2,6,2,4,4,7,2,8,2,6,4,4,2,9,2,4,6,6,2,8,2,10,4,4,
%T A304751 4,11,2,4,4,9,2,8,2,6,8,4,2,12,4,4,4,6,2,11,2,9,4,4,2,11,2,4,8,13,4,8,
%U A304751 2,6,2,8,2,14,2,4,8,6,2,8,2,12,2,4,2,11,4,4,2,9,2,15,2,6,4,4,4,16,2,8,6,6,2,8,2,9,8
%N A304751 Filter sequence: Restricted growth sequence transform of function that gives the least natural number with the same prime signature that (0,1)-polynomial encoded in the binary expansion of n has when it is factored over Q.
%H A304751 Antti Karttunen, <a href="/A304751/b304751.txt">Table of n, a(n) for n = 1..65537</a>
%F A304751 For all i, j: a(i) = a(j) => A206719(i) = A206719(j).
%F A304751 For all i, j: a(i) = a(j) => A257000(i) = A257000(j).
%o A304751 (PARI)
%o A304751 up_to = 65537;
%o A304751 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 A304751 Aux304751(n) = { my(p=0, f=vecsort((factor(Pol(binary(n)))[, 2]), , 4)); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }
%o A304751 v304751 = rgs_transform(vector(up_to,n,Aux304751(n)));
%o A304751 A304751(n) = v304751[n];
%Y A304751 Cf. A206719, A206074 (gives the positions of 2's), A257000.
%Y A304751 Cf. also A046523 (A101296), A278233, A284010, A284011.
%K A304751 nonn
%O A304751 1,2
%A A304751 _Antti Karttunen_, Jun 08 2018