A369047 Lexicographically earliest infinite sequence such that a(i) = a(j) => A003415(i) = A003415(j) and A345000(i) = A345000(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, 20, 2, 38, 2, 40, 41, 42, 43, 44, 2, 45, 46, 47, 2, 48, 2, 31, 49, 21, 43, 50, 2, 51, 52, 53, 2, 54, 39, 34, 55, 56, 2, 57

Offset: 1

Author

Antti Karttunen, Jan 21 2024

Keywords

• nonn

Comments

Restricted growth sequence transform of the ordered pair [A003415(n), A345000(n)], or equally, of the pair [A003415(n), A369038(n)], or equally, of the pair [A345000(n), A369038(n)].

For all i, j >= 1:

A351236(i) = A351236(j) => a(i) = a(j),

a(i) = a(j) => A369034(i) = A369034(j),

a(i) = a(j) => A369036(i) = A369036(j).

Links

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

Crossrefs

Cf. A003415, A345000, A369034, A369036, A369038.

Cf. also A351236, A369051.

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]));
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A345000(n) = gcd(A003415(n),A003415(A276086(n)));
Aux369047(n) = [A003415(n), A345000(n)];
v369047 = rgs_transform(vector(up_to, n, Aux369047(n)));
A369047(n) = v369047[n];