A273058 - OEIS

%I #30 Jan 14 2017 16:55:54

%S 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 27,28,29,30,31,32,33,34,35,37,38,39,40,41,42,43,44,45,46,47,48,49,50,

%U 51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70

%N Numbers having pairwise coprime exponents in their canonical prime factorization.

%C The complement of A072413.

%H Giuseppe Coppoletta, <a href="/A273058/b273058.txt">Table of n, a(n) for n = 1..10000</a>

%F A005361(a(n)) = A072411(a(n)).

%e 36 is not a term because 36 = 2^2 * 3^2 and gcd(2,2) = 2 > 1.

%e 360 is a term because 360 = 2^3 * 3^2 * 5 and gcd(3,2) = gcd(2,1) = 1.

%e 10800 is not a term because 10800 = 2^4 * 3^3 * 5^2 and gcd(4,2) > 1

%t Select[Range@ 120, LCM @@ # == Times @@ # &@ Map[Last, FactorInteger@ #] &] (* _Michael De Vlieger_, May 15 2016 *)

%o (Sage) def d(n):

%o     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     return diff

%o [k for k in (1..100) if d(k)==0]

%o (PARI) is(n)=my(f=factor(n)[,2]); factorback(f)==lcm(f) \\ _Charles R Greathouse IV_, Jan 14 2017

%Y Cf. A005361, A072411, A130091, A072413.

%K nonn

%O 1,2

%A _Giuseppe Coppoletta_, May 14 2016