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A286533 Restricted growth sequence of A278533 (prime-signature of A253563).

%I A286533 #6 May 17 2017 17:56:07
%S A286533 1,2,3,2,4,5,3,2,6,7,7,5,4,5,3,2,8,9,10,7,9,11,7,5,6,7,7,5,4,5,3,2,12,
%T A286533 13,14,9,14,15,10,7,13,15,15,11,9,11,7,5,8,9,10,7,9,11,7,5,6,7,7,5,4,
%U A286533 5,3,2,16,17,18,13,19,20,14,9,18,21,21,15,14,15,10,7,17,20,21,15,20,22,15,11,13,15,15,11,9,11,7,5,12,13,14,9,14,15,10,7
%N A286533 Restricted growth sequence of A278533 (prime-signature of A253563).
%H A286533 Antti Karttunen, <a href="/A286533/b286533.txt">Table of n, a(n) for n = 0..65537</a>
%o A286533 (PARI)
%o A286533 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 A286533 write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
%o A286533 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ This function from _Charles R Greathouse IV_, Aug 17 2011
%o A286533 A061395(n) = if(1==n, 0, primepi(vecmax(factor(n)[, 1]))); \\ After _M. F. Hasler_'s code for A006530.
%o A286533 A253550(n) = if(1==n, 1, (n/prime(A061395(n)))*prime(1+A061395(n)));
%o A286533 A253560(n) = if(1==n, 1, (n*prime(A061395(n))));
%o A286533 A253563(n) = if(n<2,(1+n),if(!(n%2),A253560(A253563(n/2)),A253550(A253563((n-1)/2)))); \\ Would be better if memoized!
%o A286533 A278533(n) = A046523(A253563(n));
%o A286533 write_to_bfile(0,rgs_transform(vector(65538,n,A278533(n-1))),"b286533.txt");
%Y A286533 Cf. A046523, A253563, A286531, A286535, A286622.
%K A286533 nonn
%O A286533 0,2
%A A286533 _Antti Karttunen_, May 17 2017