A132350 - OEIS

%I #30 Jun 01 2018 15:31:57

%S 1,1,1,0,1,1,1,0,0,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,0,1,0,1,1,1,1,0,1,1,

%T 1,0,1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,

%U 1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0

%N If n > 1 is a k-th power with k >= 2 then a(n) = 0, otherwise a(n) = 1.

%H Antti Karttunen, <a href="/A132350/b132350.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = 1 - A075802(n) for n >= 2. - _R. J. Mathar_, Nov 12 2007

%F Given the Möbius function mu(n) = A008683(n), a(n) = abs(mu(n)) unless n is in A303946. - _Alonso del Arte_, May 28 2018

%e a(4) = 0 because 4 = 2^2.

%e a(8) = 0 because 8 = 2^3.

%e a(12) = 1 because 12 is not a perfect power (though it is divisible by a perfect power).

%t Table[Boole[GCD@@FactorInteger[n][[All, 2]] == 1], {n, 100}] (* _Alonso del Arte_, May 28 2018 *)

%o (PARI) (a(n)=!ispower(n)); (r(nMax) = for(j=1,nMax,print1(!ispower(j)","))); r(100)

%o (Haskell)

%o a132350 1 = 1

%o a132350 n = 1 - a075802 n  -- _Reinhard Zumkeller_, Jun 14 2013

%Y Cf. A132349, A132351, A132352, A075802, A001597.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Nov 11 2007

%E Edited by _M. F. Hasler_, Jun 01 2018