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A305815 Restricted growth sequence transform of A305814, a filter sequence constructed from the GF(2)[X]-factorization signatures of the divisors of n.

%I A305815 #8 Jun 12 2018 10:16:02
%S A305815 1,2,2,3,4,5,2,6,7,8,2,9,2,5,6,10,11,12,2,13,14,5,15,16,3,5,17,9,15,
%T A305815 16,2,18,5,19,20,21,2,5,22,23,2,24,15,9,25,26,2,27,7,9,28,9,15,29,14,
%U A305815 16,22,26,2,30,2,5,9,31,32,33,2,34,20,35,15,36,2,5,37,9,5,38,15,39,40,5,41,42,43,26,5,16,15,44,45,46,5,5,8,47,2,12,48,49,41,50
%N A305815 Restricted growth sequence transform of A305814, a filter sequence constructed from the GF(2)[X]-factorization signatures of the divisors of n.
%H A305815 Antti Karttunen, <a href="/A305815/b305815.txt">Table of n, a(n) for n = 1..65537</a>
%H A305815 <a href="/index/Ge#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%F A305815 For all i, j:
%F A305815   a(i) = a(j) => A000005(i) = A000005(j).
%F A305815   a(i) = a(j) => A294883(i) = A294883(j).
%F A305815   a(i) = a(j) => A294884(i) = A294884(j).
%o A305815 (PARI)
%o A305815 \\ Needs also code from A305788:
%o A305815 up_to = 65537;
%o A305815 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 A305815 A305814(n) = { my(m=1); fordiv(n, d, if(d>1, m *= prime(A305788(d)-1))); (m); };
%o A305815 v305815 = rgs_transform(vector(up_to, n, A305814(n)));
%o A305815 A305815(n) = v305815[n];
%Y A305815 Cf. A278233, A305788, A305813, A305814.
%Y A305815 Cf. also A305795.
%K A305815 nonn
%O A305815 1,2
%A A305815 _Antti Karttunen_, Jun 11 2018