A112964 -id:A112964 - cp's OEIS frontend

A112966 Sum(mu(i)*omega(j): i+j=n), with mu=A008683 and omega=A001221.

0, 0, 1, 0, -1, -1, -1, -2, -3, -2, -2, -1, -3, -3, -4, 0, -6, -1, -4, -1, -3, -3, -7, 0, -5, -3, -3, 0, -5, 1, -5, -2, -10, -1, -8, 4, -8, -3, -4, 2, -6, 0, -5, -1, -4, -2, -11, 3, -8, -1, -8, -1, -11, 2, -8, 2, -7, -3, -9, 5, -2, -5, -7, 2, -11, 7, -6, 0, -4, 1, -9, 4, -12, -3, -6, 0, -10, 2, -7, -1, -10, -8, -12, 6, -13, -2, -12, 0

Offset: 1

Reinhard Zumkeller, Oct 07 2005

			a(5)=mu(1)*omega(4)+mu(2)*omega(3)+mu(3)*omega(2)+mu(4)*omega(1)
= 1*1 - 1*1 - 1*1 + 0*0 = -1.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A013939, A112965, A068341, A112962, A112963, A112964, A112968.

a112966 n = sum $ zipWith (*)
   a008683_list $ reverse $ take (n - 1) a001221_list
-- Reinhard Zumkeller, Feb 29 2012

A112968 a(n) = Sum_{i+j=n} mu(i)*Omega(j), with mu=A008683 and Omega=A001222.

Original entry on oeis.org

0, 0, 1, 0, 0, -2, -2, -2, -2, -2, -6, -2, -4, -2, -7, -1, -5, 0, -7, -3, -9, 1, -11, 2, -7, 1, -12, 1, -11, 7, -8, -5, -8, -1, -18, 3, -10, 1, -13, 1, -7, 13, -12, -2, -13, 6, -16, 3, -11, 3, -15, -4, -16, 13, -15, -4, -15, 4, -17, 11, -14, 4, -13, 7, -12, 15, -17, -5, -15, 16, -13, 3, -12, 3, -20, 3, -27, 19, -20, -3, -11, 3

Offset: 1

Reinhard Zumkeller, Oct 07 2005

			a(5) = mu(1)*Omega(4)+mu(2)*Omega(3)+mu(3)*Omega(2)+mu(4)*Omega(1) = 1*2 - 1*1 - 1*1 + 0*1 = 0.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A013939, A112967, A068341, A112962, A112963, A112964, A112966.

a112968 n = sum $ zipWith (*)
   a008683_list $ reverse $ take (n - 1) a001222_list
-- Reinhard Zumkeller, Feb 29 2012

A112968[n_]:=Plus@@Table[MoebiusMu[i]*PrimeOmega[n-i],{i,1,n-1}]; Array[A112968,200] (* Enrique Pérez Herrero, Feb 28 2012 *)

Corrected by N. J. A. Sloane, Mar 01 2006

A112963 Sum(mu(i)*tau(j): i+j=n), with mu=A008683 and tau=A000005.

Original entry on oeis.org

0, 1, 1, -1, -1, -4, -2, -5, -5, -4, -7, -4, -6, -7, -11, 0, -12, -1, -11, -6, -12, -1, -20, 2, -13, -2, -16, 2, -19, 9, -18, -9, -20, 4, -31, 10, -21, -2, -18, 7, -20, 14, -26, -3, -16, 13, -40, 5, -26, 7, -22, -1, -40, 18, -32, 2, -21, 10, -40, 16, -25, 5, -21, 17, -41, 31, -40, -4, -14, 30, -38, 3, -39, 8, -21, 14, -58

Offset: 1

Reinhard Zumkeller, Oct 07 2005

sign

			a(5)=mu(1)*tau(4)+mu(2)*tau(3)+mu(3)*tau(2)+mu(4)*tau(1)
= 1*3 - 1*2 - 1*2 + 0*1 = -1.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A006218, A055507, A068341, A112962, A112964, A112966, A112968.

a112963 n = sum $ zipWith (*)
   a008683_list $ reverse $ take (n - 1) a000005_list
-- Reinhard Zumkeller, Feb 29 2012

A112962 Sum(mu(i)*phi(j): i+j=n), with mu=A008683 and phi=A000010.

Original entry on oeis.org

0, 1, 0, 0, -1, -1, -4, -2, -5, -8, -5, -8, -9, -11, -10, -24, 1, -21, -11, -23, -15, -37, 4, -42, -11, -38, -7, -49, 6, -63, -12, -44, -3, -81, 10, -106, 7, -49, -8, -92, 15, -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

Offset: 1

Reinhard Zumkeller, Oct 07 2005

sign

			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.

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

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

a(n)=sum(i=1,n-1,moebius(i)*eulerphi(n-i)) \\ Charles R Greathouse IV, Feb 21 2013

Corrected by N. J. A. Sloane, Mar 01 2006

cp's OEIS Frontend

A112966 Sum(mu(i)*omega(j): i+j=n), with mu=A008683 and omega=A001221.

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A112968 a(n) = Sum_{i+j=n} mu(i)*Omega(j), with mu=A008683 and Omega=A001222.

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A112963 Sum(mu(i)*tau(j): i+j=n), with mu=A008683 and tau=A000005.

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Haskell

A112962 Sum(mu(i)*phi(j): i+j=n), with mu=A008683 and phi=A000010.

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