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

0,4

Comments

Restricted growth sequence transform of A324186.

Links

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

Formula

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

Prog

(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];

Crossrefs

Cf. A000265, A000593, A163511, A324186.

Cf. also A366804.

Sequence in context: A347374 A336934 A366874 * A366881 A366891 A003602

Adjacent sequences: A366803 A366804 A366805 * A366807 A366808 A366809

Keyword

nonn

Author

Antti Karttunen, Oct 26 2023

Status

approved