A076700 Number of prime powers of prime numbers less than 10^n.

3, 7, 18, 40, 88, 208, 513, 1345, 3605, 9965, 27984, 79815, 230184, 669541, 1961782, 5781027, 17121898, 50926700, 152037454, 455379086, 1367866472, 4119420084, 12434683582, 37613680284, 113995431428, 346090115288, 1052421037283, 3205047207003, 9774084239631

Offset: 1

Author

Zak Seidov, Oct 26 2002

Keywords

• nonn

Examples

			a(2) = 7 because 4, 8, 9, 25, 27, 32 and 49 are the only prime powers of prime numbers less than 100.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..34

Crossrefs

Cf. A053810, A075308.

Programs

Mathematica

pp = Sort[ Flatten[ Table[ Prime[n]^Prime[i], {n, 1, PrimePi[ Sqrt[10^17]]}, {i, 1, PrimePi[ Floor[ Log[ Prime[n], 10^17]]]}]]]; a = {}; k = 1; Do[ While[ pp[[k]] <= 10^n, k++ ]; a = Append[a, k-1], {n, 1, 17}]

Python

from sympy import primepi, integer_nthroot, primerange
def A076700(n): return int(sum(primepi(integer_nthroot(10**n, p)[0]) for p in primerange((10**n).bit_length()))) # Chai Wah Wu, Sep 12 2024

Extensions

Edited and extended by Robert G. Wilson v, Oct 31 2002

a(18), a(19) from Ray Chandler, Oct 30 2008

a(20)-a(29) from Donovan Johnson, Mar 12 2013