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 A045763 Number of numbers "unrelated to n": m < n such that m is neither a divisor of n nor relatively prime to n. 54
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,10 COMMENTS Suggested by Wouter Meeussen. a(n) = 0 iff n is a prime or 1 or 4. - Robert G. Wilson v, Nov 02 2005 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). - Farideh Firoozbakht, Dec 23 2014 LINKS T. D. Noe and Michael De Vlieger, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe) Martin Beumer, The Arithmetical Function tau_k(N), Amer. Math. Monthly, 69, Oct 1962, p. 780 (a(n)=ksi(N)). FORMULA 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 MAPLE A045763 := proc(n)     n+1-numtheory[tau](n)-numtheory[phi](n) ; end proc: seq(A045763(n), n=1..100); # Robert Israel, Dec 23 2014 MATHEMATICA f[n_] := n + 1 - DivisorSigma[0, n] - EulerPhi[n]; Array[f, 84] (* Robert G. Wilson v *) PROG (PARI) a(n)=n+1-numdiv(n)-eulerphi(n) \\ Charles R Greathouse IV, Jul 15 2011 CROSSREFS Cf. A000005, A000010, A133995. Sequence in context: A272727 A323135 A100258 * A132748 A022901 A055945 Adjacent sequences:  A045760 A045761 A045762 * A045764 A045765 A045766 KEYWORD nonn,look AUTHOR EXTENSIONS More terms from Robert G. Wilson v, Nov 02 2005 STATUS approved

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Last modified October 15 12:23 EDT 2019. Contains 328026 sequences. (Running on oeis4.)