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%I #40 Dec 11 2021 14:36:45
%S 1,6,36,120,1296,1260,46656,7560,44100,45360,60466176,110880,
%T 2176782336,1632960,1587600,1081080,2821109907456,3880800,
%U 101559956668416,6486480,57153600,2116316160,131621703842267136,21621600,1944810000,76187381760
%N Smallest number with exactly n^2 divisors.
%C For n = prime see A061234.
%H David A. Corneth, <a href="/A061707/b061707.txt">Table of n, a(n) for n = 1..330</a> (first 44 terms from Amiram Eldar)
%F a(n) = Min_{x : d(x) = n^2} = A005179(A000290(n)).
%F Also: A000005(a(n)) = A000290(n).
%F a(prime(n)) = A061234(n). - _Bernard Schott_, Jun 21 2019
%e n = 6: a(6) = 1260 = 2*2*3*3*5*7 and d(1260) = 36.
%t 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 *)
%o (PARI) a(n) = {my(k = 1); while (numdiv(k) != n^2, k++); k;} \\ _Michel Marcus_, Sep 05 2017
%Y Cf. A000005, A000040, A000290, A005179, A061234, A300357 (1st bisection).
%K nonn
%O 1,2
%A _Labos Elemer_, Jun 19 2001
%E More terms from _Don Reble_, Nov 08 2001
%E Offset corrected by _Hagen von Eitzen_, Jun 05 2009
%E a(24)-a(26) from _Ray Chandler_, Jun 19 2009
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