A374131 Lexicographically earliest infinite sequence such that for all i, j >= 1, a(i) = a(j) => f(i) = f(j), where f(1) = 1, and for n > 1, f(n) = [A083345(n), A374132(n), A374133(n)], where A083345 is the numerator of the fully additive function with a(p) = 1/p, and A374132 and A374133 are the 2- and 3-adic valuations of A276085, which is fully additive with a(p) = p#/p.

1, 2, 3, 3, 4, 5, 4, 6, 7, 8, 4, 9, 4, 10, 11, 7, 4, 8, 4, 12, 13, 14, 4, 15, 16, 17, 4, 18, 4, 19, 4, 20, 21, 22, 23, 24, 4, 25, 26, 27, 4, 28, 4, 29, 30, 31, 4, 32, 16, 10, 33, 34, 4, 35, 36, 37, 38, 39, 4, 40, 4, 41, 42, 43, 44, 45, 4, 46, 47, 48, 4, 14, 4, 49, 50, 33, 51, 52, 4, 50, 53, 54, 4, 55, 56, 57, 58, 59, 4, 60, 61, 62, 63, 64, 65, 66, 4, 15, 67, 68

Offset: 1

Author

Antti Karttunen, Jun 30 2024

Keywords

• nonn

Comments

Restricted growth sequence transform of the function f given in the definition.

For all i, j >= 1:

A305900(i) = A305900(j) => a(i) = a(j),

a(i) = a(j) => A035263(i) = A035263(j),

a(i) = a(j) => A369001(i) = A369001(j),

a(i) = a(j) => A369004(i) = A369004(j),

a(i) = a(j) => A372573(i) = A372573(j),

a(i) = a(j) => A373137(i) = A373137(j),

a(i) = a(j) => A373258(i) = A373258(j),

a(i) = a(j) => A373483(i) = A373483(j).

Links

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

Crossrefs

Cf. A083345, A374132, A374133.

Cf. A035263, A305900, A369001, A369004, A372573, A373137, A373258, A373483.

Cf. also 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; };
A083345(n) = { my(f=factor(n)); numerator(vecsum(vector(#f~, i, 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))); };
Aux374131(n) = if(1==n, n, my(u=A276085(n)); [A083345(n), valuation(u, 2), valuation(u, 3)]);
v374131 = rgs_transform(vector(up_to, n, Aux374131(n)));
A374131(n) = v374131[n];