A356008 A variant of Look and Say sequence (A005150) based on exponents in prime factorization of n (see Comments section for precise definition).

1, 6, 105, 12, 315, 18, 945, 24, 525, 6006, 2835, 420, 8505, 42042, 735, 48, 25515, 1050, 76545, 12012, 440895, 294294, 229635, 840, 1575, 2060058, 2625, 84084, 688905, 54, 2066715, 96, 5731635, 14420406, 2205, 36, 6200145, 100942842, 74511255, 24024, 18600435

Offset: 1

Author

Rémy Sigrist, Jul 23 2022

Keywords

• nonn

Comments

To compute a(n):

- a(1) = 1,

- for n > 1:

- consider the prime factorization of n:

n = Product_{i = 1..k} prime(i)^e_i

(where e_k > 0 and prime(i) denotes the i-th prime number),

- apply the Look and Say procedure to the list (e_k, ..., e_1),

- the result, say (f_m, ..., f_1), gives the prime exponents for a(n):

a(n) = Product_{i = 1..m} prime(i)^f_i.

There are only two fixed points: a(1) = 1 and a(36) = 36.

All terms are distinct and belong to A244990 (but some terms of A244990, like 210 = 7*5*3*2, do not appear here).

Examples

			For n = 99:
- 99 = 11^1 * 7^0 * 5^0 * 3^2 * 2^0,
- the list of exponents is: 1 0 0 2 0,
- applying the Look and Say procedure, we obtain: 1 1 2 0 1 2 1 0,
- so a(99) = 19^1 * 17^1 * 13^2 * 11^0 * 7^1 * 5^2 * 3^1 * 2^0 = 28658175.
		

Links

• Rémy Sigrist, PARI program

Crossrefs

Cf. A002110, A005150, A007814, A008776, A067255, A244990, A356014, A356016.

Programs

PARI

See Links section.

Formula

a(n) = n mod 2.

A007814(a(n)) = A007814(n).

a(prime(n)) = 7*5*3^(n-1) for any n > 1.

a(A002110(n)) = 2*3^n = A008776(n) for any n > 0.