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A076700
Number of prime powers of prime numbers less than 10^n.
1
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
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
Sequence in context: A074587 A208715 A302408 * A265007 A026533 A131630
KEYWORD
nonn
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