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A140635 Smallest positive integer having the same number of divisors as n.

%I A140635 #19 Aug 31 2023 12:16:03
%S A140635 1,2,2,4,2,6,2,6,4,6,2,12,2,6,6,16,2,12,2,12,6,6,2,24,4,6,6,12,2,24,2,
%T A140635 12,6,6,6,36,2,6,6,24,2,24,2,12,12,6,2,48,4,12,6,12,2,24,6,24,6,6,2,
%U A140635 60,2,6,12,64,6,24,2,12,6,24,2,60,2,6,12,12,6,24,2,48,16,6,2,60,6,6,6,24,2
%N A140635 Smallest positive integer having the same number of divisors as n.
%C A140635 a(n) <= n for all n. Moreover, a(n) = n if and only if n belongs to A005179 or A007416.
%H A140635 Antti Karttunen, <a href="/A140635/b140635.txt">Table of n, a(n) for n = 1..10000</a>
%F A140635 a(n) = A005179(A000005(n)).
%t A140635 a140635[n_] := NestWhile[#+1&, 1, DivisorSigma[0, n]!=DivisorSigma[0, #]&]
%t A140635 a140635[{m_, n_}] := Map[a140635, Range[m, n]]
%t A140635 a140635[{1, 89}] (* _Hartmut F. W. Hoft_, Jun 13 2023 *)
%o A140635 (PARI) A140635(n) = { my(nd = numdiv(n)); for (i=1, n, if (numdiv(i) == nd, return (i))); }; \\ After A139770, _Antti Karttunen_, May 27 2017
%o A140635 (Python)
%o A140635 from sympy import divisor_count as d
%o A140635 def a(n):
%o A140635     x=d(n)
%o A140635     m=1
%o A140635     while True:
%o A140635         if d(m)==x: return m
%o A140635         else: m+=1 # _Indranil Ghosh_, May 27 2017
%Y A140635 Cf. A000005, A005179, A007416, A139770.
%Y A140635 Cf. A019505, A138113, A061300 (sequences that can be defined in terms of this sequence).
%K A140635 nonn
%O A140635 1,2
%A A140635 _Max Alekseyev_, May 19 2008