cp's OEIS Frontend

A366878 Lexicographically earliest infinite sequence such that a(i) = a(j) => A366875(i) = A366875(j) for all i, j >= 0.

%I A366878 #6 Oct 27 2023 13:12:01
%S A366878 1,2,3,4,3,1,5,6,3,2,2,2,3,7,8,9,3,10,1,11,3,12,1,9,3,10,13,14,3,15,
%T A366878 12,16,3,6,17,18,3,19,20,21,3,1,9,22,3,23,12,24,3,25,17,26,3,27,28,29,
%U A366878 3,10,30,23,3,31,32,11,3,11,8,33,3,34,35,36,3,11,37,38,3,39,40,41,3,5,2,42,3,43,44,45,3,1,46,47,3
%N A366878 Lexicographically earliest infinite sequence such that a(i) = a(j) => A366875(i) = A366875(j) for all i, j >= 0.
%C A366878 Restricted growth sequence transform of A366875.
%H A366878 Antti Karttunen, <a href="/A366878/b366878.txt">Table of n, a(n) for n = 0..65537</a>
%o A366878 (PARI)
%o A366878 up_to = 65537;
%o A366878 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 A366878 A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
%o A366878 A113415(n) = if(n<1, 0, sumdiv(n, d, if(d%2, (d+1)/2)));
%o A366878 memoA349915 = Map();
%o A366878 A349915(n) = if(1==n,1,my(v); if(mapisdefined(memoA349915,n,&v), v, v = -sumdiv(n,d,if(d<n,A113415(n/d)*A349915(d),0)); mapput(memoA349915,n,v); (v)));
%o A366878 A366875(n) = A349915(A163511(n));
%o A366878 v366878 = rgs_transform(vector(1+up_to,n,A366875(n-1)));
%o A366878 A366878(n) = v366878[1+n];
%Y A366878 Cf. A113415, A163511, A349915, A366875.
%Y A366878 Cf. also A366383, A366874.
%K A366878 nonn
%O A366878 0,2
%A A366878 _Antti Karttunen_, Oct 27 2023