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A069637
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Number of prime powers <= n with exponents > 1.
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6
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0, 0, 0, 1, 1, 1, 1, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10
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OFFSET
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1,8
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COMMENTS
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REFERENCES
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H. Sahu, K. Kar and B.S.K.R. Somayajulu, On the average order of pi*(n) - pi(n), Acta Cienc. Indica Math., Vol. 11 (1985), pp. 165-168.
József Sándor, Dragoslav S. Mitrinovic and Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, Chapter VII, p. 237.
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LINKS
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FORMULA
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Sum_{k=1..n} a(k) ~ (4/3) * n^(3/2)/log(n) + O(n^(3/2)/log(n)^2) (Sahu et al., 1985). - Amiram Eldar, Mar 07 2021
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MAPLE
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with(numtheory);
A069637 := proc(N) local ct, i; ct:=0;
for i from 1 to N do if not isprime(i) and nops(factorset(i))=1 then ct:=ct+1; fi; od; ct; end; # N. J. A. Sloane, Jun 05 2022
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MATHEMATICA
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Table[Sum[PrimePi[n^(1/k)], {k, Log[2, n]}]-PrimePi[n], {n, 94}] (* Stefano Spezia, Jun 05 2022 *)
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PROG
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(SageMath)
(Python)
from sympy import primepi, integer_nthroot
def A069637(n): return sum(primepi(integer_nthroot(n, k)[0]) for k in range(2, n.bit_length())) # Chai Wah Wu, Aug 15 2024
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CROSSREFS
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KEYWORD
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nonn,changed
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AUTHOR
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STATUS
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approved
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