A112962 - OEIS

%I #9 Feb 21 2013 02:10:56

%S 0,1,0,0,-1,-1,-4,-2,-5,-8,-5,-8,-9,-11,-10,-24,1,-21,-11,-23,-15,-37,

%T 4,-42,-11,-38,-7,-49,6,-63,-12,-44,-3,-81,10,-106,7,-49,-8,-92,15,

%U -103,2,-72,-5,-114,41,-140,-3,-114,8,-113,49,-179,3,-135,27,-131,46,-218,-7,-99,32,-185,72,-259,50,-104,23,-211,52,-248,43,-153

%N Sum(mu(i)*phi(j): i+j=n), with mu=A008683 and phi=A000010.

%e a(5)=mu(1)*phi(4)+mu(2)*phi(3)+mu(3)*phi(2)+mu(4)*phi(1) = 1*2 - 1*2 - 1*1 + 0*1 = -1.

%p with(numtheory); f:=n->add(phi(i)*mobius(n-i),i=1..n-1);

%o (PARI) a(n)=sum(i=1,n-1,moebius(i)*eulerphi(n-i)) \\ _Charles R Greathouse IV_, Feb 21 2013

%Y Cf. A002088, A065093, A068341, A112963, A112964, A112966, A112968.

%K sign

%O 1,7

%A _Reinhard Zumkeller_, Oct 07 2005

%E Corrected by _N. J. A. Sloane_, Mar 01 2006