%I A051709
%S A051709 0,0,0,1,0,2,0,3,1,2,0,8,0,2,2,7,0,9,0,10,2,2,0,20,1,2,4,12,0,20,0,15,
%T A051709 2,2,2,31,0,2,2,26,0,24,0,16,12,2,0,44,1,13,2,18,0,30,2,32,2,2,0,64,0,
%U A051709 2,14,31,2,32,0,22,2,28,0,75,0,2,14,24,2,36,0,58,13,2,0,80,2,2,2,44,0
%N A051709 sigma(n)+phi(n)-2n.
%C A051709 a(5)=sigma(5)+phi(5)-2*5 = 6+4-10 = 0.
%C A051709 Because sigma and phi are multiplicative functions, it is easy to show 
               that (1) if a(n)=0, then n is prime (or 1) and (2) if a(n)=2, then 
               n is the product of two distinct prime numbers. Note that a(n) is 
               the n-th term of the Dirichlet series whose generating function is 
               given below. Using the generating function, it is theoretically possible 
               to compute a(n). Hence a(n)=0 could be used as a primarity test and 
               a(n)=2 could be used as a test for membership in P2 (A006881). - 
               T. D. Noe (noe(AT)sspectra.com), Aug 01 2002
%H A051709 T. D. Noe, <a href="b051709.txt">Table of n, a(n) for n=1..1000</a>
%H A051709 C. Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_076.htm">
               Related problem</a>
%F A051709 Dirichlet g.f.: zeta(s-1) * (zeta(s) - 2 + 1/zeta(s)) - T. D. Noe (noe(AT)sspectra.com), 
               Aug 01 2002
%Y A051709 Cf. A000010, A000203, A005843, A006881, A065387, A072780.
%Y A051709 Sequence in context: A135818 A078804 A071465 this_sequence A054656 A080096 
               A068915
%Y A051709 Adjacent sequences: A051706 A051707 A051708 this_sequence A051710 A051711 
               A051712
%K A051709 nonn
%O A051709 1,6
%A A051709 Jud McCranie and Carlos Rivera (j.mccranie(AT)comcast.net)