A070965 a(1) = 1; a(n+1) = sum{k|n} a(k) * mu(k), where the sum is over the positive divisors, k, of n; and mu(k) is the Moebius function.

1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, -1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, -1, 2, -1, 2, 0, 0, 0, 0, 1, 0, -1, -1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 2, 0, 1, 1, 1, -1, -1, 0, 1, -1, 2, 3, 1, 0, 0, 1, 0, 0, 1, -1, 2, 1, 0, -1, 0, -1, -2, 2, -1, 1, 1, 0, 1, 1, 2, 1, 3, 0, 1, -1, -2, 0, 2, 2, 2, 1, 0, -1, 0, 1, 0, 2, -1, 0

Offset: 1

Author

Leroy Quet, May 16 2002

Keywords

• sign

Comments

Conjecture: all integers are present. - W. Edwin Clark, Aug 20 2004

a(A227953(n)) = n and a(A227954(n)) = -n. - Reinhard Zumkeller, Aug 01 2013

Examples

			a(7) = a(1) mu(1) + a(2) mu(2) + a(3) mu(3) + a(6) mu(6) = 1 - 1 - 0 + 1 = 1 because 1, 2, 3 and 6 are the divisors of 6.
		

Links

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

Crossrefs

Cf. A027750, A225817.

Programs

Haskell

a070965 n = a070965_list !! (n-1)
a070965_list = 1 : f 1 where
   f x = y : f (x + 1) where
     y = sum $ zipWith (*) (map a070965 $ a027750_row x) (a225817_row x)
-- Reinhard Zumkeller, Jul 30 2013

Maple

a:=proc(n) option remember; add(numtheory[mobius](i)*a(i),i in numtheory[divisors](n-1)) end: a(1):=1: seq(a(n),n=1..100); # Alec Mihailovs, Aug 20 2004

Mathematica

a[1] = a[2] = 1; a[n_] := a[n] = Block[{d = Divisors[n - 1]}, Plus @@ (MoebiusMu[d]*a /@ d)]; Table[ a[n], {n, 105}] (* Robert G. Wilson v, Aug 21 2004 *)

PARI

a(n)=if(n<3,1,sumdiv(n-1,k,a(k)*moebius(k))) \\ Charles R Greathouse IV, Feb 07 2013