A369046 Lexicographically earliest infinite sequence such that a(i) = a(j) => A003415(i) = A003415(j) and A069359(i) = A069359(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, 17, 18, 19, 20, 2, 21, 2, 22, 23, 24, 25, 26, 2, 27, 28, 29, 2, 30, 2, 31, 32, 33, 2, 34, 35, 36, 37, 38, 2, 39, 28, 40, 41, 21, 2, 42, 2, 43, 44, 45, 46, 47, 2, 48, 49, 50, 2, 51, 2, 52, 53, 54, 46, 55, 2, 56, 57, 58, 2, 59, 41, 60, 61, 62, 2, 63, 37

Offset: 1

Author

Antti Karttunen, Jan 18 2024

Keywords

• nonn

Comments

Restricted growth sequence transform of the ordered pair [A003415(n), A069359(n)].

For all i,j >= 1:

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

a(i) = a(j) => A329039(i) = A329039(j) => A008966(i) = A008966(j).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A003415, A008966, A069359, A329039.

Cf. also A369050, A369051.

Differs from A351236 for the first time at n=91, where a(91) = 37, while A351236(91) = 64.

Differs from A344025 for the first time at n=140, where a(140) = 97, while A344025(140) = 92.

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; };
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A069359(n) = (n*sumdiv(n, d, isprime(d)/d));
Aux369046(n) = [A003415(n), A069359(n)];
v369046 = rgs_transform(vector(up_to, n, Aux369046(n)));
A369046(n) = v369046[n];