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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, 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.
Sequence in context: A198477 A075178 A145618 * A169900 A140355 A007041
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Mar 05 2019
STATUS
approved

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Last modified July 19 15:03 EDT 2024. Contains 374410 sequences. (Running on oeis4.)