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A045763
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Number of numbers "unrelated to n": m < n such that m is neither a divisor of n nor relatively prime to n.
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60
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0, 0, 0, 0, 0, 1, 0, 1, 1, 3, 0, 3, 0, 5, 4, 4, 0, 7, 0, 7, 6, 9, 0, 9, 3, 11, 6, 11, 0, 15, 0, 11, 10, 15, 8, 16, 0, 17, 12, 17, 0, 23, 0, 19, 16, 21, 0, 23, 5, 25, 16, 23, 0, 29, 12, 25, 18, 27, 0, 33, 0, 29, 22, 26, 14, 39, 0, 31, 22, 39, 0, 37, 0, 35, 30, 35, 14, 47, 0, 39, 23, 39, 0, 49
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OFFSET
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1,10
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COMMENTS
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1. a(p^k) = p^(k-1) - k where p is a prime and k is a positive integer. Hence if p is prime then a(p) = 0 which is a result of the previous comment.
2. If n = 2*p or n = 4*p and p is an odd prime then a(n) = phi(n) - 1.
3. If n = 3*p where p is a prime not equal to 3 then a(n) = (1/2)*phi(n). (End)
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LINKS
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FORMULA
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a(n) = n + 1 - d(n) - phi(n), where d(n) is the number of divisors of n and phi is Euler's totient function.
Dirichlet generating function: zeta(s-1) + zeta(s) - zeta(s)^2 - zeta(s-1)/zeta(s). - Robert Israel, Dec 23 2014
a(n) = Sum_{k=1..n} (1 - floor(1/gcd(n,k))) * (ceiling(n/k) - floor(n/k)). - Wesley Ivan Hurt, Jan 06 2024
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MAPLE
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n+1-numtheory[tau](n)-numtheory[phi](n) ;
end proc:
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MATHEMATICA
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PROG
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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