A369040 Lexicographically earliest infinite sequence such that a(i) = a(j) => A003415(i) = A003415(j) and A342014(i) = A342014(j), for all i, j >= 1.

1, 2, 2, 3, 2, 4, 2, 5, 6, 7, 2, 8, 2, 9, 10, 11, 2, 12, 2, 13, 14, 15, 2, 16, 14, 17, 18, 19, 2, 20, 2, 21, 22, 23, 24, 25, 2, 26, 27, 28, 2, 29, 2, 30, 31, 32, 2, 33, 22, 34, 35, 36, 2, 37, 27, 38, 39, 40, 2, 41, 2, 42, 43, 44, 45, 46, 2, 47, 48, 49, 2, 50, 2, 31, 51, 52, 45, 53, 2, 54, 55, 56, 2, 57, 39, 34, 58, 59, 2, 60, 35

Offset

1,2

Comments

Restricted growth sequence transform of the ordered pair [A003415(n), A342014(n)].

For all i, j >= 1:

A369050(i) = A369050(j) => a(i) = a(j), [Conjectured]

a(i) = a(j) => A341625(i) = A341625(j).

Links

Antti Karttunen, Table of n, a(n) for n = 1..100000

Prog

(PARI)
up_to = 100000;
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; };
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A342014(n) = (A003415(n)%n);
Aux369040(n) = [A003415(n), A342014(n)];
v369040 = rgs_transform(vector(up_to, n, Aux369040(n)));
A369040(n) = v369040[n];

Crossrefs

Cf. A003415, A341625, A342014.

Cf. also A369040, A369050, A369051.

Sequence in context: A327970 A369448 A369047 * A328767 A319682 A329353

Adjacent sequences: A369037 A369038 A369039 * A369041 A369042 A369043

Keyword

nonn

Author

Antti Karttunen, Jan 18 2024

Status

approved