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A318887 Filter sequence related to the differences of prime factors of n.

%I A318887 #5 Sep 24 2018 17:46:04
%S A318887 1,2,2,3,2,4,2,5,3,6,2,7,2,8,9,10,2,11,2,12,13,14,2,15,3,16,5,17,2,18,
%T A318887 2,19,20,21,9,22,2,23,24,25,2,26,2,27,28,29,2,30,3,31,32,33,2,34,35,
%U A318887 36,37,38,2,39,2,40,41,42,20,43,2,44,45,46,2,47,2,48,49,50,13,51,2,52,10,53,2,54,55,56,57,58,2,59,35,60,61,62,32,63,2,64,65,66,2
%N A318887 Filter sequence related to the differences of prime factors of n.
%C A318887 Restricted growth sequence transform of A318885.
%H A318887 Antti Karttunen, <a href="/A318887/b318887.txt">Table of n, a(n) for n = 1..100000</a>
%o A318887 (PARI)
%o A318887 up_to = 100000;
%o A318887 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 A318887 A318885(n) = if(1==n,n,my(f=factor(n),m=2^f[1,2],i=1); for(k=2,#f~,i += (f[k,1]-f[k-1,1]); m *= prime(i)^f[k,2]); (m));
%o A318887 v318887 = rgs_transform(vector(up_to,n,A318885(n)));
%o A318887 A318887(n) = v318887[n];
%Y A318887 Cf. A318885, A318888.
%K A318887 nonn
%O A318887 1,2
%A A318887 _Antti Karttunen_, Sep 24 2018