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%I A338140 #31 Sep 08 2022 08:46:25
%S A338140 1,2,8,18,24,36,108,180,72,216,288,1944,360,1080,1920,720,1800,2160,
%T A338140 5400,1440,6720,3600,12600,4320,16200,5760,12960,38016,13440,45360,
%U A338140 35280,10080,21600,28800,67200,51840,215040,20160,30240,97200,50400,64800,144000
%N A338140 a(n) is the smallest number with n refactorable divisors.
%C A338140 a(n) is the greedy inverse of A336041: the smallest number with exactly n divisors d such that d / tau(d) is also an integer.
%C A338140 Numbers 1 and 2 are only numbers m such that d / tau(d) is an integer for all divisors d of m.
%F A338140 a(n) = min{ k: A336041(k)=n}. - _R. J. Mathar_, Nov 24 2020
%e A338140 a(3) = 8 because 8 with divisors 1, 2, 4 and 8 is the smallest number with 3 refactorable divisors: 1 / tau(1) = 1, 2 / tau(2) = 1, 8 / tau(8) = 2.
%t A338140 f[n_] := DivisorSum[n, 1 &, Divisible[#, DivisorSigma[0, #]] &]; m = 43; s = Table[0, {m}]; c = 0; n = 1; While[c < m, i = f[n]; If[i <= m && s[[i]] == 0, c++; s[[i]] = n]; n++]; s (* _Amiram Eldar_, Oct 24 2020 *)
%o A338140 (Magma) [Min([m: m in[1..10^5] | #[d: d in Divisors(m) | IsIntegral(d / #Divisors(d))] eq n]): n in [1..12]]
%Y A338140 Cf. A336041, A033950 (refactorable numbers).
%Y A338140 Cf. A335182, A335665.
%K A338140 nonn
%O A338140 1,2
%A A338140 _Jaroslav Krizek_, Oct 24 2020

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