A231117 - OEIS

%I #21 Nov 26 2013 18:37:17

%S 1,1,2,0,3,2,5,0,2,3,7,0,8,5,6,1,11,0,12,1,8,9,15,0,7,10,5,3,17,8,19,

%T 3,13,13,15,1,23,15,17,2,26,11,28,3,6,18,30,1,16,3,21,5,32,2,25,4,23,

%U 23,36,1,37,25,10,6,30,18,41,6,29,22,44,2,45,30,11,7,36,22,49,4,17,32

%N Number of positive integers <= n and relatively prime to n which are squarefree if and only if n is squarefree.

%H Charles R Greathouse IV, <a href="/A231117/b231117.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A073311(n) if n is squarefree or phi(n) - A073311(n) otherwise. (Where phi is given by A000010)

%F a(n) = A008966(n)*A073311(n) + A107078(n)*A073312(n). - _Antti Karttunen_, Nov 26 2013

%e a(4) = 0 because 4 is not squarefree and phi(4) - A073311(4) = 2 - 2 = 0.

%o (PARI) a(n)=my(s=sum(i=1,n,gcd(n,i)==1&&issquarefree(i))); if(issquarefree(n), s, eulerphi(n)-s) \\ _Charles R Greathouse IV_, Nov 05 2013

%Y Cf. A005117, A073311, A073312.

%K nonn

%O 1,3

%A _Irina Gerasimova_, Nov 03 2013

%E a(4) corrected and a(54) inserted by _Charles R Greathouse IV_, Nov 05 2013