cp's OEIS Frontend

A305789 Filter-sequence combining prime signature of n (A046523) and similar signature for GF(2)[X]-factorization (A278233).

%I A305789 #6 Jun 10 2018 21:15:06
%S A305789 1,2,2,3,4,5,2,6,7,8,2,9,2,5,10,11,12,13,2,14,15,5,16,17,18,5,19,9,16,
%T A305789 20,2,21,5,22,5,23,2,5,8,24,2,25,16,9,26,27,2,28,7,29,30,9,16,31,32,
%U A305789 17,8,27,2,33,2,5,9,34,35,36,2,37,15,36,16,38,2,5,26,9,5,39,16,40,41,5,42,43,44,27,32,17,16,45,32,46,5,5,8,47,2,13,9,48,42
%N A305789 Filter-sequence combining prime signature of n (A046523) and similar signature for GF(2)[X]-factorization (A278233).
%C A305789 Restricted growth sequence transform of ordered pair [A046523(n), A278233(n)].
%C A305789 For all i, j: a(i) = a(j) => A305802(i) = A305802(j).
%H A305789 Antti Karttunen, <a href="/A305789/b305789.txt">Table of n, a(n) for n = 1..65537</a>
%H A305789 <a href="/index/Ge#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%o A305789 (PARI)
%o A305789 up_to = 65537;
%o A305789 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 A305789 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
%o A305789 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 A305789 Aux305789(n) = [A046523(n), A278233(n)];
%o A305789 v305789 = rgs_transform(vector(up_to,n,Aux305789(n)));
%o A305789 A305789(n) = v305789[n];
%Y A305789 Cf. A046523, A101296, A278233, A305788, A305802.
%Y A305789 Cf. also A305790.
%K A305789 nonn
%O A305789 1,2
%A A305789 _Antti Karttunen_, Jun 10 2018