A366806 Lexicographically earliest infinite sequence such that a(i) = a(j) => A324186(i) = A324186(j) for all i, j >= 0, where A324186 is the sum of odd divisors permuted by A163511.

1, 1, 1, 2, 1, 3, 2, 4, 1, 5, 3, 6, 2, 7, 4, 8, 1, 9, 5, 10, 3, 11, 6, 12, 2, 13, 7, 14, 4, 15, 8, 16, 1, 17, 9, 18, 5, 19, 10, 20, 3, 21, 11, 22, 6, 23, 12, 24, 2, 25, 13, 26, 7, 27, 14, 28, 4, 29, 15, 30, 8, 14, 16, 31, 1, 32, 17, 33, 9, 34, 18, 35, 5, 36, 19, 37, 10, 38, 20, 39, 3, 40, 21, 41, 11, 42, 22, 43, 6

Offset: 0

Author

Antti Karttunen, Oct 26 2023

Keywords

• nonn

Comments

Restricted growth sequence transform of A324186.

Links

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

Crossrefs

Cf. A000265, A000593, A163511, A324186.

Cf. also A366804.

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; };
A000593(n) = sigma(n>>valuation(n, 2)); \\ From A000593
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));
A324186(n) = A000593(A163511(n));
v366806 = rgs_transform(vector(1+up_to,n,A324186(n-1)));
A366806(n) = v366806[1+n];

Formula

For all n >= 1, a(n) = a(2*n) = a(A000265(n)).