A373380 Lexicographically earliest infinite sequence such that a(i) = a(j) => A373145(i) = A373145(j), A373362(i) = A373362(j), and A373364(i) = A373364(j), for all i, j >= 1.

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

Offset

1,2

Comments

Restricted growth sequence transform of the triple [A373145(n), A373362(n), A373364(n)], i.e., the triple [gcd(x, y), gcd(x, z), gcd(y, z)], where x=A001414(n), y=A003415(n), z=A276085(n).

For all i, j >= 1:

A305800(i) = A305800(j) => a(i) = a(j),

a(i) = a(j) => A373367(i) = A373367(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; };
A001414(n) = ((n=factor(n))[, 1]~*n[, 2]);
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*prod(i=1, primepi(f[k, 1]-1), prime(i))); };
Aux373380(n) = { my(x=A001414(n), y=A003415(n), z=A276085(n)); [gcd(x, y), gcd(x, z), gcd(y, z)]; };
v373380 = rgs_transform(vector(up_to, n, Aux373380(n)));
A373380(n) = v373380[n];

Crossrefs

Cf. A001414, A003415, A276085, A305800, A373145, A373362, A373364, A373367.

Cf. also A373150, A373379.

Sequence in context: A323240 A300229 A300825 * A355000 A300232 A351235

Adjacent sequences: A373377 A373378 A373379 * A373381 A373382 A373383

Keyword

nonn

Author

Antti Karttunen, Jun 03 2024

Status

approved