A356008 - OEIS

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

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OFFSET

1,2

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).

LINKS

Table of n, a(n) for n=1..41.

Rémy Sigrist, PARI program

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.

EXAMPLE

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.

PROG

(PARI) See Links section.

CROSSREFS

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

Sequence in context: A055969 A285027 A184188 * A112822 A033589 A077289

Adjacent sequences: A356005 A356006 A356007 * A356009 A356010 A356011

KEYWORD

nonn

AUTHOR

Rémy Sigrist, Jul 23 2022

STATUS

approved