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%I #7 Jun 10 2018 21:14:59
%S 1,2,2,3,3,4,2,5,4,6,2,6,2,4,5,7,7,8,2,9,3,4,4,10,2,4,6,6,4,10,2,11,4,
%T 12,4,13,2,4,6,14,2,6,4,6,10,8,2,12,4,4,11,6,4,13,2,10,6,8,2,14,2,4,6,
%U 15,9,8,2,16,3,8,4,17,2,4,10,6,4,13,4,16,3,4,8,9,15,8,2,10,4,17,2,13,4,4,6,18,2,8,6,6,8,18,2,10,10
%N Restricted growth sequence transform of A278233, filter-sequence for GF(2)[X]-factorization.
%C This is GF(2)[X] analog of A101296.
%H Antti Karttunen, <a href="/A305788/b305788.txt">Table of n, a(n) for n = 1..65537</a>
%H <a href="/index/Ge#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%o (PARI)
%o up_to = 65537;
%o 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 A278233(n) = { my(p=0, f=vecsort((factor(Pol(binary(n))*Mod(1, 2))[, 2]), , 4)); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };
%o v305788 = rgs_transform(vector(up_to,n,A278233(n)));
%o A305788(n) = v305788[n];
%Y Cf. A278233.
%Y Cf. A014580 (positions of 2's).
%Y Cf. also A101296, A304529, A304751, A305789.
%K nonn
%O 1,2
%A _Antti Karttunen_, Jun 10 2018
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