

A045763


Number of numbers "unrelated to n": m < n such that m is neither a divisor of n nor relatively prime to n.


53



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^(k1)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(s1) + zeta(s)  zeta(s)^2  zeta(s1)/zeta(s).  Robert Israel, Dec 23 2014


MAPLE

A045763 := proc(n)
n+1numtheory[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+1numdiv(n)eulerphi(n) \\ Charles R Greathouse IV, Jul 15 2011


CROSSREFS

Cf. A000005, A000010, A133995.
Sequence in context: A240923 A272727 A100258 * A132748 A022901 A055945
Adjacent sequences: A045760 A045761 A045762 * A045764 A045765 A045766


KEYWORD

nonn,look


AUTHOR

N. J. A. Sloane


EXTENSIONS

More terms from Robert G. Wilson v, Nov 02 2005


STATUS

approved



