A366874 Lexicographically earliest infinite sequence such that a(i) = a(j) => A366873(i) = A366873(j) for all i, j >= 0, where A366873 is the average of number of and sum of odd divisors of n as 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, 3, 1, 31, 17, 32, 9, 33, 18, 34, 5, 35, 19, 36, 10, 37, 20, 38, 3, 39, 21, 40, 11, 41, 22, 42, 6

Offset

0,4

Comments

Restricted growth sequence transform of A366873.

Links

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

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; };
A113415(n) = if(n<1, 0, sumdiv(n, d, if(d%2, (d+1)/2)));
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));
A366873(n) = A113415(A163511(n));
v366874 = rgs_transform(vector(1+up_to, n, A366873(n-1)));
A366874(n) = v366874[1+n];

Crossrefs

Cf. A113415, A163511, A366873.

Cf. also A366798, A366806, A366878.

Sequence in context: A351040 A347374 A336934 * A366806 A366881 A366891

Adjacent sequences: A366871 A366872 A366873 * A366875 A366876 A366877

Keyword

nonn

Author

Antti Karttunen, Oct 27 2023

Status

approved