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 A351058 Number of numbers <= n that are either nonprime divisors of n or primes not dividing n. 0
 1, 1, 2, 3, 3, 3, 4, 6, 5, 4, 5, 7, 6, 6, 6, 9, 7, 9, 8, 10, 8, 8, 9, 13, 10, 9, 11, 11, 10, 12, 11, 15, 11, 11, 11, 16, 12, 12, 12, 16, 13, 15, 14, 16, 16, 14, 15, 21, 16, 17, 15, 17, 16, 20, 16, 20, 16, 16, 17, 23, 18, 18, 20, 23, 18, 20, 19, 21, 19, 21, 20, 28, 21, 21, 23 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS a(p) = pi(p) for p prime. LINKS Table of n, a(n) for n=1..75. FORMULA a(n) = n - Sum_{k=1..n} [u(n/k) = v(k)], where u(n) = 1 - ceiling(n) + floor(n), v is the prime characteristic (A010051), and [ ] is the Iverson bracket. EXAMPLE a(8) = 6; 1 is nonprime and divides 8, 3 does not divide 8 and is prime, 4 is not prime and divides 8, 5 is prime and does not divide 8, 7 is prime and does not divide 8, and 8 (nonprime) divides itself. So a(8) = 6. PROG (PARI) a(n) = sum(k=1, n, bitxor(isprime(k)&&(n%k), !isprime(k)&&!(n%k))); \\ Michel Marcus, Jan 31 2022 CROSSREFS Cf. A010051. Sequence in context: A108932 A029067 A048460 * A036017 A029066 A174522 Adjacent sequences: A351055 A351056 A351057 * A351059 A351060 A351061 KEYWORD nonn AUTHOR Wesley Ivan Hurt, Jan 30 2022 STATUS approved

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Last modified September 29 03:24 EDT 2023. Contains 365749 sequences. (Running on oeis4.)