A373150 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(1) = 1, and for n>1, f(n) = [A003415(n), A085731(n), A373148(n)], 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, 42, 2, 43, 2, 44, 45, 46, 47, 48, 2, 49, 50, 51, 2, 52, 2, 53, 54, 55, 56, 57, 2, 58, 59, 60, 2, 61, 62, 63, 64, 65, 2, 66, 67, 68, 69, 70, 71, 72, 2, 73, 74

Offset: 1

Author

Antti Karttunen, May 27 2024

Keywords

• nonn

Comments

Restricted growth sequence transform of the function f defined as: f(1) = 1, and for n>1, f(n) = [A003415(n), A085731(n), A373148(n)].

For all i, j >= 1:

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

a(i) = a(j) => A369051(i) = A369051(j),

a(i) = a(j) => A373151(i) = A373151(j) => A373143(i) = A373143(j).

Links

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

Crossrefs

Cf. A003415, A002110, A085731, A276085, A373148.

Cf. A305800, A369051, A373143, A373151.

Differs from A369050 for the first time at n=91, where a(91)=67, while A369050(91)=37.

Differs from A300833 for the first time at n=133, where a(133)=133, while A300833(133)=50.

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]));
A085731(n) = gcd(A003415(n),n);
A002110(n) = prod(i=1,n,prime(i));
A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*A002110(primepi(f[k, 1])-1)); };
A373148(n) = (A276085(n)%A003415(n));
Aux373150(n) = if(1==n,1,[A003415(n), A085731(n), A373148(n)]);
v373150 = rgs_transform(vector(up_to, n, Aux373150(n)));
A373150(n) = v373150[n];