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A085972
Number of numbers <= n that are primes or not prime powers.
3
0, 1, 2, 2, 3, 4, 5, 5, 5, 6, 7, 8, 9, 10, 11, 11, 12, 13, 14, 15, 16, 17, 18, 19, 19, 20, 20, 21, 22, 23, 24, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 54, 55, 56, 57, 58, 59, 60, 61
OFFSET
1,3
COMMENTS
a(n) = Max{k: A085971(k)<=n};
a(n) = n-A085501(n) = A000720(n)+n-A065515(n) = A085970(n)+A000720(n).
MATHEMATICA
Accumulate[Table[If[PrimeQ[n]||(!PrimePowerQ[n]), 1, 0], {n, 80}]]-1 (* Harvey P. Dale, Oct 13 2022 *)
PROG
(Python)
from sympy import primepi, integer_nthroot
def A085972(n): return n-1-sum(primepi(integer_nthroot(n, k)[0]) for k in range(2, n.bit_length())) # Chai Wah Wu, Aug 20 2024
CROSSREFS
Sequence in context: A242493 A261345 A243285 * A136378 A344374 A305557
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Jul 06 2003
STATUS
approved