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A319355 Filter sequence constructed from the lengths of arithmetic progressions occurring among the divisors of n.

%I A319355 #7 Sep 23 2018 20:59:39
%S A319355 1,2,2,3,2,4,2,5,3,5,2,6,2,5,4,7,2,8,2,9,5,5,2,10,3,5,5,11,2,12,2,9,5,
%T A319355 5,5,13,2,5,5,14,2,15,2,9,16,5,2,17,3,9,5,9,2,18,5,15,5,5,2,19,2,5,9,
%U A319355 20,5,18,2,9,5,21,2,22,2,5,8,9,5,15,2,23,7,5,2,24,5,5,5,21,2,25,4,9,5,5,5,26,2,9,9,27,2,15,2,21,28
%N A319355 Filter sequence constructed from the lengths of arithmetic progressions occurring among the divisors of n.
%C A319355 Restricted growth sequence transform of A319354.
%C A319355 For all i, j:
%C A319355   a(i) = a(j) => A067131(i) = A067131(j).
%C A319355   a(i) = a(j) => A160752(i) = A160752(j).
%C A319355   a(i) = a(j) => A091009(i) = A091009(j).
%H A319355 Antti Karttunen, <a href="/A319355/b319355.txt">Table of n, a(n) for n = 1..65537</a>
%o A319355 (PARI)
%o A319355 up_to = 65537;
%o A319355 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 A319355 A319354(n) = if(1==n,2,my(d=divisors(n),m=1); for(i=1,(#d-1), for(j=(i+1),#d,my(c=1,k=d[j],s=(d[j]-d[i])); while(!(n%k), k+=s; c++); m *= prime(c))); (m));
%o A319355 v319355 = rgs_transform(vector(up_to,n,A319354(n)));
%o A319355 A319355(n) = v319355[n];
%Y A319355 Cf. A319354.
%K A319355 nonn
%O A319355 1,2
%A A319355 _Antti Karttunen_, Sep 21 2018