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

1,1

Links

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

Example

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

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}]

Prog

(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

Crossrefs

Cf. A053810, A075308.

Sequence in context: A074587 A208715 A302408 * A265007 A026533 A131630

Adjacent sequences: A076697 A076698 A076699 * A076701 A076702 A076703

Keyword

nonn,changed

Author

Zak Seidov, Oct 26 2002

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

Status

approved