A347374 Lexicographically earliest infinite sequence such that a(i) = a(j) => A331410(i) = A331410(j) and A000593(i) = A000593(j), for all i, j >= 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, 17, 5, 18, 10, 19, 3, 20, 11, 21, 6, 22, 12, 23, 2, 24, 13, 25, 7, 26, 14, 25, 4, 27, 15, 28, 8, 29, 16, 30, 1, 31, 17, 32, 9, 33, 17, 34, 5, 35, 18, 36, 10, 33, 19, 37, 3, 38, 20, 39, 11, 40, 21, 41, 6, 42, 22, 43, 12

Offset

1,3

Comments

Restricted growth sequence transform of the ordered pair [A000593(n), A331410(n)].

For all i, j: A003602(i) = A003602(j) => a(i) = a(j) => A347249(i) = A347249(j).

Links

Antti Karttunen, Table of n, a(n) for n = 1..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; };
A000593(n) = sigma(n>>valuation(n, 2));
A331410(n) = { my(f=factor(n)); sum(k=1, #f~, if(2==f[k, 1], 0, f[k, 2]*(1+A331410(f[k, 1]+1)))); };
Aux347374(n) = [A331410(n), A000593(n)];
v347374 = rgs_transform(vector(up_to, n, Aux347374(n)));
A347374(n) = v347374[n];

Crossrefs

Cf. A000593, A003602, A331410, A347249.

Cf. also A335880, A336390, A336391, A336394 for similar constructions.

Sequence in context: A351035 A351036 A351040 * A336934 A366874 A366806

Adjacent sequences: A347371 A347372 A347373 * A347375 A347376 A347377

Keyword

nonn

Author

Antti Karttunen, Aug 29 2021

Status

approved