A231117 Number of positive integers <= n and relatively prime to n which are squarefree if and only if n is squarefree.

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, 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, 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

Offset: 1

Author

Irina Gerasimova, Nov 03 2013

Keywords

• nonn

Examples

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

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005117, A073311, A073312.

Programs

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

Formula

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

a(n) = A008966(n)*A073311(n) + A107078(n)*A073312(n). - Antti Karttunen, Nov 26 2013

Extensions

a(4) corrected and a(54) inserted by Charles R Greathouse IV, Nov 05 2013