A369067 Lexicographically earliest infinite sequence such that a(i) = a(j) => A369066(i) = A369066(j) for all i, j >= 0.

1, 2, 2, 1, 2, 3, 2, 3, 2, 4, 5, 1, 2, 6, 1, 7, 2, 8, 9, 1, 10, 11, 4, 9, 2, 6, 3, 1, 6, 1, 12, 5, 2, 13, 14, 1, 11, 15, 8, 11, 16, 17, 18, 1, 8, 19, 1, 20, 2, 6, 3, 1, 4, 4, 6, 4, 6, 5, 9, 1, 6, 8, 2, 20, 2, 21, 11, 1, 16, 22, 13, 15, 23, 24, 25, 1, 13, 21, 1, 26, 27, 28, 29, 1, 30, 29, 17, 31, 13, 21, 15, 1, 16

Offset: 0

Author

Antti Karttunen, Jan 16 2024

Keywords

• nonn

Comments

Restricted growth sequence transform of A369066.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..65537

Crossrefs

Cf. A005940, A008836, A083345, A369066, A369069.

Cf. also A366805 (compare the scatter plots).

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); };
A008836(n) = ((-1)^bigomega(n));
A083345(n) = { my(f=factor(n)); numerator(vecsum(vector(#f~, i, f[i, 2]/f[i, 1]))); };
A369069(n) = sumdiv(n,d,A008836(n/d)*A083345(d));
A369066(n) = A369069(A005940(1+n));
v369067 = rgs_transform(vector(1+up_to,n,A369066(n-1)));
A369067(n) = v369067[1+n];