A373152 Lexicographically earliest infinite sequence such that a(i) = a(j) => A085731(i) = A085731(j) and A373145(i) = A373145(j), for all i, j >= 1.

1, 2, 2, 3, 2, 2, 2, 4, 5, 6, 2, 7, 2, 2, 8, 9, 2, 10, 2, 11, 12, 2, 2, 13, 14, 2, 15, 16, 2, 2, 2, 17, 12, 2, 18, 19, 2, 2, 8, 13, 2, 2, 2, 7, 10, 2, 2, 20, 21, 22, 23, 11, 2, 24, 8, 13, 12, 2, 2, 3, 2, 2, 25, 26, 27, 2, 2, 11, 12, 2, 2, 28, 2, 2, 22, 29, 27, 2, 2, 20, 30, 2, 2, 3, 12, 2, 8, 13, 2, 10, 31, 7, 12, 2, 18, 32, 2, 33, 10, 34, 2, 2, 2, 13, 2

Offset: 1

Author

Antti Karttunen, Jun 03 2024

Keywords

• nonn

Comments

Restricted growth sequence transform of the ordered pair [A085731(n), A373145(n)], i.e., the ordered pair [gcd(n, A003415(n)), gcd(A003415(n), A276085(n))].

For all i, j >= 1: A373150(i) = A373150(j) => a(i) = a(j).

Links

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

Crossrefs

Cf. A085731, A276085, A373145.

Cf. also A373150, A373151.

Programs

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]));
A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*prod(i=1,primepi(f[k, 1]-1),prime(i))); };
Aux373152(n) = [gcd(n, A003415(n)), gcd(A003415(n), A276085(n))];
v373152 = rgs_transform(vector(up_to, n, Aux373152(n)));
A373152(n) = v373152[n];