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A273058 Numbers having pairwise coprime exponents in their canonical prime factorization.

%I A273058 #30 Jan 14 2017 16:55:54
%S A273058 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,
%T A273058 27,28,29,30,31,32,33,34,35,37,38,39,40,41,42,43,44,45,46,47,48,49,50,
%U A273058 51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70
%N A273058 Numbers having pairwise coprime exponents in their canonical prime factorization.
%C A273058 The complement of A072413.
%H A273058 Giuseppe Coppoletta, <a href="/A273058/b273058.txt">Table of n, a(n) for n = 1..10000</a>
%F A273058 A005361(a(n)) = A072411(a(n)).
%e A273058 36 is not a term because 36 = 2^2 * 3^2 and gcd(2,2) = 2 > 1.
%e A273058 360 is a term because 360 = 2^3 * 3^2 * 5 and gcd(3,2) = gcd(2,1) = 1.
%e A273058 10800 is not a term because 10800 = 2^4 * 3^3 * 5^2 and gcd(4,2) > 1
%t A273058 Select[Range@ 120, LCM @@ # == Times @@ # &@ Map[Last, FactorInteger@ #] &] (* _Michael De Vlieger_, May 15 2016 *)
%o A273058 (Sage) def d(n):
%o A273058     v=factor(n)[:]; L=len(v); diff=prod(v[j][1] for j in range(L)) - lcm([v[j][1] for j in range(L)])
%o A273058     return diff
%o A273058 [k for k in (1..100) if d(k)==0]
%o A273058 (PARI) is(n)=my(f=factor(n)[,2]); factorback(f)==lcm(f) \\ _Charles R Greathouse IV_, Jan 14 2017
%Y A273058 Cf. A005361, A072411, A130091, A072413.
%K A273058 nonn
%O A273058 1,2
%A A273058 _Giuseppe Coppoletta_, May 14 2016