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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, 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: A198477 A075178 A145618 * A169900 A140355 A007041 Adjacent sequences:  A306690 A306691 A306692 * A306694 A306695 A306696 KEYWORD nonn AUTHOR Rémy Sigrist, Mar 05 2019 STATUS approved

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Last modified May 18 23:31 EDT 2022. Contains 353826 sequences. (Running on oeis4.)