Voozh

VOOZH

URL: https://oeis.org/A306693

⇱ A306693 - OEIS

login

A306693

a(n) is the least strongly refactorable multiple of n if any, or a(n) = -1 otherwise.

1

1, 2, 12, 12, 240, 12, 3360, 24, 36, 240, 5280, 12, 6240, 3360, 240, 240, 8160, 36, 9120, 240, 3360, 5280, 11040, 24, 21600, 6240, 4320, 3360, 13920, 240, 14880, 480, 5280, 8160, 3360, 36, 17760, 9120, 6240, 240, 19680, 3360, 20640, 5280, 720, 11040, 22560

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Strongly refactorable numbers correspond to A141586.

Is a(n) > 0 for any n > 0 ?

LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, Colored logarithmic scatterplot of the first 100000 terms (where the color is function of A000005(n))

FORMULA

a(A141586(n)) = A141586(n) for any n > 0.

EXAMPLE

For n = 3:

- the divisors of 3 are: 1, 3,

- the corresponding numbers of divisors are: 1, 2,

- 2 does not divide 3,

- the divisors of 2*3 are: 1, 2, 3, 6,

- the corresponding numbers of divisors are: 1, 2, 2, 4,

- 4 does not divide 2*3,

- the divisors of 2*2*3 are: 1, 2, 3, 4, 6, 12,

- the corresponding numbers of divisors are: 1, 2, 2, 3, 4, 6,

- they all divide 2*2*3,

- hence a(3) = 2*2*3 = 12.

PROG

(PARI) a(n) = while (1, my (m=n); fordiv (m, d, m=lcm(m, numdiv(d))); if (n==m, return (n), n=m))

CROSSREFS

See A306645 for a similar sequence.

Cf. A000005, A141586.

Sequence in context: A075178 A392539 A145618 * A169900 A140355 A007041

Adjacent sequences: A306690 A306691 A306692 * A306694 A306695 A306696

KEYWORD

nonn

AUTHOR

Rémy Sigrist, Mar 05 2019

STATUS

approved