A306693 a(n) is the least strongly refactorable multiple of n if any, or a(n) = -1 otherwise.

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

Offset: 1

Author

Rémy Sigrist, Mar 05 2019

Keywords

• nonn

Comments

Strongly refactorable numbers correspond to A141586.

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

Examples

			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.
		

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))

Crossrefs

See A306645 for a similar sequence.

Cf. A000005, A141586.

Programs

PARI

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

Formula

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