A076048 Number of prime powers p^k (k != 1) <= 10^n.

1, 4, 11, 26, 52, 109, 237, 556, 1405, 3690, 10085, 28157, 80071, 230568, 670122, 1962690, 5782468, 17124206, 50930440, 152043592, 455389240, 1367883344, 4119448337, 12434731102, 37613760490, 113995567275, 346090346047, 1052421430209

Offset: 0

Author

Robert G. Wilson v, Oct 29 2002

Keywords

• nonn

Examples

			a(2)=11 because 1, 4, 8, 9, 16, 25, 27, 32, 49, 64 & 81 are the only prime powers less than 100.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 0..40

Crossrefs

Cf. A025475.

Programs

Mathematica

f[n_] := Block[{t = 1, k = 2}, While[s = PrimePi[10^(n/k)]; s != 0, t = t + s; k++ ]; t]; Table[ f[n], {n, 0, 27}]

PARI

a(n)=my(N=10^n); sum(k=2,logint(N,2),primepi(sqrtnint(N,k)))+1 \\ Charles R Greathouse IV, Jul 21 2017

Extensions

a(16)-a(27) from David Wasserman, Mar 13 2005

a(23) corrected by Charles R Greathouse IV, Jul 21 2017