cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A061707 Smallest number with exactly n^2 divisors.

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%I A061707 #49 Feb 04 2025 07:16:21
%S A061707 1,6,36,120,1296,1260,46656,7560,44100,45360,60466176,110880,
%T A061707 2176782336,1632960,1587600,1081080,2821109907456,3880800,
%U A061707 101559956668416,6486480,57153600,2116316160,131621703842267136,21621600,1944810000,76187381760
%N A061707 Smallest number with exactly n^2 divisors.
%C A061707 For n = prime see A061234.
%H A061707 Amiram Eldar, <a href="/A061707/b061707.txt">Table of n, a(n) for n = 1..1288</a> (terms 1..44 from Amiram Eldar, terms 45..330 from David A. Corneth)
%F A061707 a(n) = Min_{x : d(x) = n^2} = A005179(A000290(n)).
%F A061707 A000005(a(n)) = A000290(n).
%F A061707 a(prime(n)) = A061234(n). - _Bernard Schott_, Jun 21 2019
%F A061707 a(n) = A005179(n^2). - _Amiram Eldar_, Feb 04 2025
%e A061707 For n = 6: a(6) = 1260 = 2*2*3*3*5*7 and d(1260) = 36.
%t A061707 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 A061707 (PARI) a(n) = {my(k = 1); while (numdiv(k) != n^2, k++); k;} \\ _Michel Marcus_, Sep 05 2017
%Y A061707 Cf. A000005, A000040, A000290, A005179, A061234, A300357 (1st bisection).
%K A061707 nonn
%O A061707 1,2
%A A061707 _Labos Elemer_, Jun 19 2001
%E A061707 More terms from _Don Reble_, Nov 08 2001
%E A061707 Offset corrected by _Hagen von Eitzen_, Jun 05 2009
%E A061707 a(24)-a(26) from _Ray Chandler_, Jun 19 2009