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.

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, 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, 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

Offset: 0

Author

Antti Karttunen, Oct 27 2023

Keywords

• nonn

Comments

Restricted growth sequence transform of A366799.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..65537
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A005940, A320111, A366799.

Cf. also A366798.

Programs

PARI

up_to = 65537;
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; };
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
A320111(n) = sumdiv(n,d,(2!=(d%4)));
A366799(n) = A320111(A005940(1+n));
v366800 = rgs_transform(vector(1+up_to,n,A366799(n-1)));
A366800(n) = v366800[1+n];