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A338140 a(n) is the smallest number with n refactorable divisors. 0
1, 2, 8, 18, 24, 36, 108, 180, 72, 216, 288, 1944, 360, 1080, 1920, 720, 1800, 2160, 5400, 1440, 6720, 3600, 12600, 4320, 16200, 5760, 12960, 38016, 13440, 45360, 35280, 10080, 21600, 28800, 67200, 51840, 215040, 20160, 30240, 97200, 50400, 64800, 144000 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
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.
Numbers 1 and 2 are only numbers m such that d / tau(d) is an integer for all divisors d of m.
LINKS
FORMULA
a(n) = min{ k: A336041(k)=n}. - R. J. Mathar, Nov 24 2020
EXAMPLE
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.
MATHEMATICA
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 *)
PROG
(Magma) [Min([m: m in[1..10^5] | #[d: d in Divisors(m) | IsIntegral(d / #Divisors(d))] eq n]): n in [1..12]]
CROSSREFS
Cf. A336041, A033950 (refactorable numbers).
Sequence in context: A117612 A320662 A171613 * A306394 A109136 A295522
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Oct 24 2020
STATUS
approved

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Last modified July 21 09:38 EDT 2024. Contains 374472 sequences. (Running on oeis4.)