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A122375 Number of distinct prime factors of the smallest number with exactly n divisors.

%I A122375 #24 Dec 11 2021 02:10:41
%S A122375 0,1,1,2,1,2,1,2,2,2,1,3,1,2,2,3,1,3,1,3,2,2,1,3,2,2,3,3,1,3,1,4,2,2,
%T A122375 2,4,1,2,2,4,1,3,1,3,3,2,1,4,2,3,2,3,1,4,2,4,2,2,1,4,1,2,3,4,2,3,1,3,
%U A122375 2,3,1,4,1,2,3,3,2,3,1,4,4,2,1,4,2,2,2,4,1,4,2,3,2,2,2,5,1,3,3,4,1,3,1,4,3
%N A122375 Number of distinct prime factors of the smallest number with exactly n divisors.
%C A122375 a(n) = 1 iff n is prime.
%H A122375 David A. Corneth, <a href="/A122375/b122375.txt">Table of n, a(n) for n = 1..10000</a> (first 2000 terms from Antti Karttunen)
%F A122375 a(n) = omega(A005179(n)), where omega(n) = A001221(n).
%F A122375 a(n) = A001221(A130279(n)). - _Reinhard Zumkeller_, May 21 2007
%e A122375 a(14) = 2 as A005179(14) = 192 which has 2 distinct prime divisors (2 and 3). - _David A. Corneth_, Dec 10 2021
%t A122375 A005179 = Cases[Import["https://oeis.org/A005179/b005179.txt", "Table"], {_, _}][[All, 2]];
%t A122375 a[n_] := PrimeNu[A005179[[n]]];
%t A122375 a /@ Range[2000] (* _Jean-François Alcover_, Mar 06 2020 *)
%Y A122375 Cf. A001221, A005179, A038457, A122810, A130279.
%K A122375 nonn
%O A122375 1,4
%A A122375 _Lekraj Beedassy_, Aug 30 2006
%E A122375 Edited and extended by _Ray Chandler_, Sep 11 2006