A380460 Lexicographically earliest infinite sequence such that a(i) = a(j) => A380459(i) = A380459(j), for all i, j >= 1, where A380459(n) = Product_{d|n} A276086(d)^A349394(n/d).

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, 8, 40, 41, 21, 2, 42, 2, 43, 44, 45, 46, 47, 2, 48, 49, 50, 2, 51, 2, 52, 53, 54, 46, 55, 2, 56, 57, 58, 2, 59, 60, 61, 20, 62, 2, 63, 64, 65, 66, 67, 68, 69, 2, 70, 71

Offset: 1

Author

Antti Karttunen, Jan 31 2025

Keywords

• nonn

Comments

Restricted growth sequence transform of A380459.

For all i, j >= 1:

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

a(i) = a(j) => A003415(i) = A003415(j),

a(i) = a(j) => A380467(i) = A380467(j),

a(i) = a(j) => A380477(i) = A380477(j).

Links

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

Crossrefs

Cf. A276086, A349394, A380459.

Cf. A003415, A305800, A380467, A380477.

Cf. also A329351, A329381.

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; };
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A349394(n) = { my(p=0, e); if((e=isprimepower(n, &p)), p^(e-1), 0); };
A380459(n) = { my(m=1); fordiv(n, d, m *= A276086(d)^A349394(n/d)); (m); };
v380460 = rgs_transform(vector(up_to, n, A380459(n)));
A380460(n) = v380460[n];