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A061707
Smallest number with exactly n^2 divisors.
3
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
OFFSET
1,2
COMMENTS
For n = prime see A061234.
LINKS
David A. Corneth, Table of n, a(n) for n = 1..330 (first 44 terms from Amiram Eldar)
FORMULA
a(n) = Min_{x : d(x) = n^2} = A005179(A000290(n)).
Also: A000005(a(n)) = A000290(n).
a(prime(n)) = A061234(n). - Bernard Schott, Jun 21 2019
EXAMPLE
n = 6: a(6) = 1260 = 2*2*3*3*5*7 and d(1260) = 36.
MATHEMATICA
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 *)
PROG
(PARI) a(n) = {my(k = 1); while (numdiv(k) != n^2, k++); k; } \\ Michel Marcus, Sep 05 2017
CROSSREFS
Cf. A000005, A000040, A000290, A005179, A061234, A300357 (1st bisection).
Sequence in context: A375608 A083374 A264366 * A253945 A331576 A056375
KEYWORD
nonn
AUTHOR
Labos Elemer, Jun 19 2001
EXTENSIONS
More terms from Don Reble, Nov 08 2001
Offset corrected by Hagen von Eitzen, Jun 05 2009
a(24)-a(26) from Ray Chandler, Jun 19 2009
STATUS
approved