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A318832 Restricted growth sequence transform of A278222(A000203(n)).

%I A318832 #5 Sep 05 2018 06:13:07
%S A318832 1,2,1,3,2,2,1,4,5,6,2,3,3,2,2,7,6,8,6,9,1,6,2,4,7,9,6,3,4,6,1,10,2,
%T A318832 11,2,12,5,4,3,13,9,2,5,9,8,6,2,7,8,14,6,5,11,4,6,4,6,13,4,9,7,2,5,15,
%U A318832 9,6,6,10,2,6,6,11,9,8,7,5,2,9,6,14,16,10,9,3,11,6,4,13,13,14,3,9,1,6,4,10,5,17,8,12,11,11,5,13,2
%N A318832 Restricted growth sequence transform of A278222(A000203(n)).
%C A318832 Sequence allots a distinct value for each distinct multiset formed from the lengths of 1-runs in the binary representation of A000203(n).
%C A318832 For all i, j: a(i) = a(j) => A175548(i) = A175548(j).
%H A318832 Antti Karttunen, <a href="/A318832/b318832.txt">Table of n, a(n) for n = 1..65537</a>
%H A318832 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%o A318832 (PARI)
%o A318832 up_to = 65537;
%o A318832 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 A318832 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
%o A318832 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
%o A318832 A278222(n) = A046523(A005940(1+n));
%o A318832 v318832 = rgs_transform(vector(up_to,n,A278222(sigma(n))));
%o A318832 A318832(n) = v318832[n];
%Y A318832 Cf. A000203, A278222.
%Y A318832 Cf. also A286622, A304101, A318831.
%K A318832 nonn
%O A318832 1,2
%A A318832 _Antti Karttunen_, Sep 04 2018