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A061707
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Smallest number with exactly n^2 divisors.
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3
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1, 6, 36, 120, 1296, 1260, 46656, 7560, 44100, 45360, 60466176, 110880, 2176782336, 1632960, 1587600, 1081080, 2821109907456, 3880800, 101559956668416, 6486480, 57153600, 2116316160, 131621703842267136, 21621600, 1944810000, 76187381760
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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EXAMPLE
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n = 6: a(6) = 1260 = 2*2*3*3*5*7 and d(1260) = 36.
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MATHEMATICA
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a[n_]:=(f=Flatten[Table@@@FactorInteger[n^2]]; Min[Times@@(Prime@Range@Length[s=Reverse@#-1]^s)&/@Union[Flatten[(ff=#; Union[Sort/@(Times@@@TakeList[ff, #]&/@Flatten[Permutations/@IntegerPartitions[Length@f], 1])])&/@Permutations@f, 1]]]); Array[a, 26] (* Giorgos Kalogeropoulos, Dec 10 2021 *)
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PROG
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(PARI) a(n) = {my(k = 1); while (numdiv(k) != n^2, k++); k; } \\ Michel Marcus, Sep 05 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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