A356068 Number of integers ranging from 1 to n that are not prime-powers (1 is not a prime-power).

1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 5, 6, 6, 6, 7, 7, 8, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 14, 15, 16, 17, 18, 18, 19, 20, 21, 21, 22, 22, 23, 24, 25, 25, 26, 26, 27, 28, 29, 29, 30, 31, 32, 33, 34, 34, 35, 35, 36, 37, 37, 38, 39, 39, 40, 41, 42

Offset: 1

Author

Gus Wiseman, Jul 31 2022

Keywords

• nonn

Examples

			The a(30) = 14 numbers: 1, 6, 10, 12, 14, 15, 18, 20, 21, 22, 24, 26, 28, 30.
		

Crossrefs

The complement is counted by A025528, with 1's A065515.

For primes instead of prime-powers we have A062298, with 1's A065855.

The version treating 1 as a prime-power is A085970.

One more than the partial sums of A143731.

A000688 counts factorizations into prime-powers.

A001222 counts prime-power divisors.

A246655 lists the prime-powers (A000961 includes 1), towers A164336.

Cf. A000720, A023894, A036234, A050361, A054685, A069513, A355743, A356064, A356065, A356066.

Programs

Mathematica

Table[Length[Select[Range[n],!PrimePowerQ[#]&]],{n,100}]

Formula

a(n) = A085970(n) + 1.