A070965 - OEIS

%I #19 Feb 14 2015 12:34:05

%S 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,

%T 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,

%U 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

%N 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.

%C Conjecture: all integers are present. - _W. Edwin Clark_, Aug 20 2004

%C a(A227953(n)) = n and a(A227954(n)) = -n. - _Reinhard Zumkeller_, Aug 01 2013

%H Reinhard Zumkeller, <a href="/A070965/b070965.txt">Table of n, a(n) for n = 1..10000</a>

%e 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.

%p 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

%t 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 *)

%o (PARI) a(n)=if(n<3,1,sumdiv(n-1,k,a(k)*moebius(k))) \\ _Charles R Greathouse IV_, Feb 07 2013

%o (Haskell)

%o a070965 n = a070965_list !! (n-1)

%o a070965_list = 1 : f 1 where

%o    f x = y : f (x + 1) where

%o      y = sum $ zipWith (*) (map a070965 $ a027750_row x) (a225817_row x)

%o -- _Reinhard Zumkeller_, Jul 30 2013

%Y Cf. A027750, A225817.

%K sign

%O 1,30

%A _Leroy Quet_, May 16 2002