cp's OEIS Frontend

A366800 Lexicographically earliest infinite sequence such that a(i) = a(j) => A366799(i) = A366799(j) for all i, j >= 0, where A366799 is the number of divisors d of n that are not of the form 4k+2, as permuted by the Doudna sequence.

%I A366800 #7 Oct 27 2023 16:38:50
%S A366800 1,1,2,2,2,2,3,3,2,2,4,4,3,3,4,4,2,2,4,4,4,4,5,5,3,3,5,5,4,4,6,6,2,2,
%T A366800 4,4,4,4,5,5,4,4,7,7,5,5,7,7,3,3,5,5,5,5,8,8,4,4,7,7,6,6,5,5,2,2,4,4,
%U A366800 4,4,5,5,4,4,7,7,5,5,7,7,4,4,7,7,7,7,9,9,5,5,9,9,7,7,10,10,3,3,5,5,5,5,8,8
%N A366800 Lexicographically earliest infinite sequence such that a(i) = a(j) => A366799(i) = A366799(j) for all i, j >= 0, where A366799 is the number of divisors d of n that are not of the form 4k+2, as permuted by the Doudna sequence.
%C A366800 Restricted growth sequence transform of A366799.
%H A366800 Antti Karttunen, <a href="/A366800/b366800.txt">Table of n, a(n) for n = 0..65537</a>
%H A366800 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%o A366800 (PARI)
%o A366800 up_to = 65537;
%o A366800 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 A366800 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
%o A366800 A320111(n) = sumdiv(n,d,(2!=(d%4)));
%o A366800 A366799(n) = A320111(A005940(1+n));
%o A366800 v366800 = rgs_transform(vector(1+up_to,n,A366799(n-1)));
%o A366800 A366800(n) = v366800[1+n];
%Y A366800 Cf. A005940, A320111, A366799.
%Y A366800 Cf. also A366798.
%K A366800 nonn
%O A366800 0,3
%A A366800 _Antti Karttunen_, Oct 27 2023