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A304113 Restricted growth sequence transform of A278263(n) = A046523(A064413(n)), a filter based on the prime signature of EKG-sequence.

%I A304113 #8 May 17 2018 17:02:45
%S A304113 1,2,3,4,2,3,5,6,4,2,4,5,4,2,4,7,8,5,4,2,4,6,9,3,4,5,4,2,4,10,11,4,2,
%T A304113 4,9,4,2,4,5,7,5,4,2,4,12,5,5,7,7,3,5,13,4,4,9,4,2,4,9,4,2,4,14,15,5,
%U A304113 4,2,4,5,9,5,12,4,2,4,8,13,4,7,4,2,4,13,4,4,10,5,4,2,4,16,5,4,7,9,5,9,14,4,2,4,9,9,12,5
%N A304113 Restricted growth sequence transform of A278263(n) = A046523(A064413(n)), a filter based on the prime signature of EKG-sequence.
%C A304113 For all i, j: a(i) = a(j) => A064742(i) = A064742(j).
%C A304113 For all i, j: a(i) = a(j) => A065203(i) = A065203(j).
%H A304113 Antti Karttunen, <a href="/A304113/b304113.txt">Table of n, a(n) for n = 1..65539</a>
%H A304113 <a href="/index/Ed#EKG">Index entries for sequences related to EKG sequence</a>
%o A304113 (PARI)
%o A304113 \\ Needs also code for A064413:
%o A304113 write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
%o A304113 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 A304113 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
%o A304113 A278263(n) = A046523(A064413(n));
%o A304113 write_to_bfile(1,rgs_transform(vector(65539,n,A278263(n))),"b304113.txt");
%Y A304113 Cf. A046523, A064413, A064742, A065203, A278263, A304112.
%Y A304113 Cf. also A304115.
%K A304113 nonn
%O A304113 1,2
%A A304113 _Antti Karttunen_, May 17 2018