%I #8 Aug 01 2022 08:21:02

%S 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,

%T 14,14,15,16,17,18,18,19,20,21,21,22,22,23,24,25,25,26,26,27,28,29,29,

%U 30,31,32,33,34,34,35,35,36,37,37,38,39,39,40,41,42

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

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

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

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

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

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

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

%Y One more than the partial sums of A143731.

%Y A000688 counts factorizations into prime-powers.

%Y A001222 counts prime-power divisors.

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

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

%K nonn

%O 1,6

%A _Gus Wiseman_, Jul 31 2022