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A069654 a(1) = 1; for n > 1, a(n) = smallest number > a(n-1) having exactly n divisors.

%I A069654 #24 Feb 19 2022 01:34:46
%S A069654 1,2,4,6,16,18,64,66,100,112,1024,1035,4096,4288,4624,4632,65536,
%T A069654 65572,262144,262192,263169,269312,4194304,4194306,4477456,4493312,
%U A069654 4498641,4498752,268435456,268437200,1073741824,1073741830,1088472064,1089142784,1107225625
%N A069654 a(1) = 1; for n > 1, a(n) = smallest number > a(n-1) having exactly n divisors.
%H A069654 Jon E. Schoenfield, <a href="/A069654/b069654.txt">Table of n, a(n) for n = 1..100</a> (first 83 terms from Charles R Greathouse IV)
%o A069654 (PARI) print(1" "1); N=1; for(n=2,28, while(numdiv(N)!=n, N++); print(n" "N)) \\ _Charles R Greathouse IV_, Sep 08 2021
%o A069654 (Python)
%o A069654 from sympy import divisor_count
%o A069654 from itertools import count, islice
%o A069654 def agen(an=1, startn=1):
%o A069654     for n in count(startn):
%o A069654         while divisor_count(an) != n: an += 1
%o A069654         yield an
%o A069654 print(list(islice(agen(), 22))) # _Michael S. Branicky_, Jan 16 2022
%Y A069654 Cf. A002182, A005179.
%Y A069654 If "exactly" is changed to "at least", we get A072121.
%K A069654 nonn
%O A069654 1,2
%A A069654 _Amarnath Murthy_, Apr 04 2002
%E A069654 Corrected and extended by _Vladeta Jovovic_, Jun 19 2002
%E A069654 More terms from _David Wasserman_, Apr 21 2003
%E A069654 a(25)-a(28) corrected by _Charles R Greathouse IV_, Sep 14 2021