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A136641 a(n) is the smallest positive integer that is coprime to n and has n divisors.

%I A136641 #21 Mar 27 2022 13:37:20
%S A136641 1,3,4,15,16,175,64,105,100,567,1024,1925,4096,3645,784,945,65536,
%T A136641 13475,262144,6237,1600,295245,4194304,25025,1296,2657205,4900,40095,
%U A136641 268435456,3776773,1073741824,10395,25600,215233605,5184,175175,68719476736,1937102445,102400
%N A136641 a(n) is the smallest positive integer that is coprime to n and has n divisors.
%C A136641 Is this the same as the least index m where A090387(m) = n? - _Michel Marcus_, Mar 25 2022
%C A136641 For p prime, a(p) = 2^(p-1) for p > 2, a(2*p) = 3^(p-1)*5 for p > 5, a(3*p) = 2^(p-1)*25 for p > 3, a(5*p) = 2^(p-1)*3^4 for p >5, ... . - _Michael S. Branicky_, Mar 26 2022
%H A136641 Michael S. Branicky, <a href="/A136641/b136641.txt">Table of n, a(n) for n = 1..65</a>
%e A136641 The sequence of positive integers each with 9 divisors starts: 36, 100, 196, 225, 256, ... Now 36 is not coprime to 9. But 100, the next bigger value with 9 divisors, is. So a(9) = 100.
%o A136641 (PARI) a(n) = my(k=1); while ((gcd(n,k) != 1) || (numdiv(k) != n), k++); k; \\ _Michel Marcus_, Mar 25 2022
%o A136641 (Python)
%o A136641 from math import gcd
%o A136641 from sympy import divisor_count
%o A136641 def a(n):
%o A136641     k = 1
%o A136641     while gcd(n, k) != 1 or divisor_count(k) != n: k += 1
%o A136641     return k
%o A136641 print([a(n) for n in range(1, 19)]) # _Michael S. Branicky_, Mar 25 2022
%Y A136641 Cf. A000005, A073904, A090387.
%K A136641 nonn
%O A136641 1,2
%A A136641 _Leroy Quet_, Apr 14 2008
%E A136641 a(11)-a(36) from _Sean A. Irvine_, May 03 2010
%E A136641 a(37) and beyond from _Michael S. Branicky_, Mar 26 2022