cp's OEIS Frontend

A305813 Restricted growth sequence transform of A305812, a filter sequence constructed from the GF(2)[X]-factorization signatures of the proper divisors of n.

%I A305813 #10 Jun 12 2018 10:16:17
%S A305813 1,2,2,3,2,4,2,5,3,5,2,6,2,4,5,7,2,8,2,9,4,4,2,10,11,4,12,6,2,10,2,13,
%T A305813 4,14,5,15,2,4,4,16,2,17,2,6,18,12,2,19,3,20,14,6,2,21,5,10,4,12,2,22,
%U A305813 2,4,6,23,5,24,2,25,12,26,2,27,2,4,28,6,4,29,2,30,31,4,2,32,33,12,12,10,2,34,4,35,4,4,5,36,2,8,8,37,2,38,2,10,39
%N A305813 Restricted growth sequence transform of A305812, a filter sequence constructed from the GF(2)[X]-factorization signatures of the proper divisors of n.
%H A305813 Antti Karttunen, <a href="/A305813/b305813.txt">Table of n, a(n) for n = 1..65537</a>
%H A305813 <a href="/index/Ge#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%F A305813 For all i, j:
%F A305813   a(i) = a(j) => A000005(i) = A000005(j).
%F A305813   a(i) = a(j) => A294881(i) = A294881(j).
%F A305813   a(i) = a(j) => A294882(i) = A294882(j).
%o A305813 (PARI)
%o A305813 \\ Needs also code from A305788:
%o A305813 up_to = 65537;
%o A305813 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 A305813 A305812(n) = if(1==n,0, my(m=1); fordiv(n,d,if((d>1)&&(d<n), m *= prime(A305788(d)-1))); (m));
%o A305813 v305813 = rgs_transform(vector(up_to, n, A305812(n)));
%o A305813 A305813(n) = v305813[n];
%Y A305813 Cf. A278233, A305788, A305812, A305815.
%Y A305813 Cf. also A305793.
%K A305813 nonn
%O A305813 1,2
%A A305813 _Antti Karttunen_, Jun 11 2018