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

%I A306693 #13 Jul 12 2019 17:07:35
%S A306693 1,2,12,12,240,12,3360,24,36,240,5280,12,6240,3360,240,240,8160,36,
%T A306693 9120,240,3360,5280,11040,24,21600,6240,4320,3360,13920,240,14880,480,
%U A306693 5280,8160,3360,36,17760,9120,6240,240,19680,3360,20640,5280,720,11040,22560
%N A306693 a(n) is the least strongly refactorable multiple of n if any, or a(n) = -1 otherwise.
%C A306693 Strongly refactorable numbers correspond to A141586.
%C A306693 Is a(n) > 0 for any n > 0 ?
%H A306693 Rémy Sigrist, <a href="/A306693/b306693.txt">Table of n, a(n) for n = 1..10000</a>
%H A306693 Rémy Sigrist, <a href="/A306693/a306693.png">Colored logarithmic scatterplot of the first 100000 terms</a> (where the color is function of A000005(n))
%F A306693 a(A141586(n)) = A141586(n) for any n > 0.
%e A306693 For n = 3:
%e A306693 - the divisors of 3 are: 1, 3,
%e A306693 - the corresponding numbers of divisors are: 1, 2,
%e A306693 - 2 does not divide 3,
%e A306693 - the divisors of 2*3 are: 1, 2, 3, 6,
%e A306693 - the corresponding numbers of divisors are: 1, 2, 2, 4,
%e A306693 - 4 does not divide 2*3,
%e A306693 - the divisors of 2*2*3 are: 1, 2, 3, 4, 6, 12,
%e A306693 - the corresponding numbers of divisors are: 1, 2, 2, 3, 4, 6,
%e A306693 - they all divide 2*2*3,
%e A306693 - hence a(3) = 2*2*3 = 12.
%o A306693 (PARI) a(n) = while (1, my (m=n); fordiv (m, d, m=lcm(m, numdiv(d))); if (n==m, return (n), n=m))
%Y A306693 See A306645 for a similar sequence.
%Y A306693 Cf. A000005, A141586.
%K A306693 nonn
%O A306693 1,2
%A A306693 _Rémy Sigrist_, Mar 05 2019