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A320117 Filter sequence for counting the residue classes mod 6 of divisors of n.

%I A320117 #7 Oct 08 2018 08:09:56
%S A320117 1,2,3,4,5,6,7,8,9,10,5,11,7,12,13,14,5,15,7,16,17,10,5,18,19,12,20,
%T A320117 21,5,22,7,23,13,10,24,25,7,12,17,26,5,27,7,16,28,10,5,29,30,31,13,21,
%U A320117 5,32,24,33,17,10,5,34,7,12,35,36,24,22,7,16,13,37,5,38,7,12,39,21,24,27,7,40,41,10,5,42,24,12,13,26,5,43,44,16,17,10,24,45,7,46,28,47,5,22,7,33
%N A320117 Filter sequence for counting the residue classes mod 6 of divisors of n.
%C A320117 Restricted growth sequence transform of A320116.
%C A320117 For all i, j:
%C A320117   A319717(i) = A319717(j) => a(i) = a(j),
%C A320117   A319996(i) = A319996(j) => a(i) = a(j),
%C A320117   A320113(i) = A320113(j) => a(i) = a(j),
%C A320117   a(i) = a(j) => A002324(i) = A002324(j).
%H A320117 Antti Karttunen, <a href="/A320117/b320117.txt">Table of n, a(n) for n = 1..100000</a>
%o A320117 (PARI)
%o A320117 up_to = 100000;
%o A320117 rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
%o A320117 A320116(n) = { my(m=1); fordiv(n,d,if(d>1, m *= prime(1+(d%6)))); (m); };
%o A320117 v320117 = rgs_transform(vector(up_to,n,A320116(n)));
%o A320117 A320117(n) = v320117[n];
%Y A320117 Cf. A319717, A319996, A320109, A320113, A320115, A320116.
%K A320117 nonn
%O A320117 1,2
%A A320117 _Antti Karttunen_, Oct 06 2018