A304573 Number of non-perfect powers (A007916) less than n and relatively prime to n.

0, 0, 1, 1, 2, 1, 4, 3, 3, 2, 6, 3, 8, 4, 5, 6, 11, 5, 13, 6, 8, 8, 17, 7, 15, 9, 13, 8, 21, 7, 23, 12, 14, 12, 17, 10, 27, 14, 18, 13, 31, 10, 33, 16, 19, 18, 37, 14, 33, 16, 25, 19, 42, 15, 31, 20, 29, 23, 48, 14, 50, 25, 30, 27, 38, 17, 55, 27, 36, 21, 59

Offset: 1

Author

Gus Wiseman, May 14 2018

Keywords

• nonn

Examples

			The a(21) = 8 positive integers less than and relatively prime to 21 that are not perfect powers are {2, 5, 10, 11, 13, 17, 19, 20}.
		

Crossrefs

Cf. A000005, A000010, A000961, A001597, A005117, A007916, A008683, A073311, A139555, A304326, A304362, A304574, A304575, A304576.

Programs

Mathematica

Table[Length[Select[Range[2,n],And[GCD@@FactorInteger[#][[All,2]]==1,GCD[n,#]==1]&]],{n,50}]

PARI

a(n) = sum(k=2, n-1, !ispower(k) && (gcd(n, k) == 1)); \\ Michel Marcus, May 15 2018