Search: id:A070965
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%I A070965
%S A070965 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,
%T A070965 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,
%U A070965 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
%V A070965 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,
%W A070965 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,
%X A070965 -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 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.
%C A070965 Conjecture: all integers are present - Edwin Clark Aug 20 2004
%H A070965 Leroy Quet, <a href="http://www.prism-of-spirals.net/">Home Page</a> 
               (listed in lieu of email address)
%e A070965 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 A070965 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); (from Alec Mihailovs Aug 20 2004)
%t A070965 a[1] = a[2] = 1; a[n_] := a[n] = Block[{d = Divisors[n - 1]}, Plus @@ 
               (MoebiusMu[d]*a /@ d)]; Table[ a[n], {n, 105}] (from Robert G. Wilson 
               v Aug 21 2004)
%Y A070965 Sequence in context: A164810 A089538 A152439 this_sequence A079548 A079071 
               A050602
%Y A070965 Adjacent sequences: A070962 A070963 A070964 this_sequence A070966 A070967 
               A070968
%K A070965 sign
%O A070965 1,30
%A A070965 Leroy Quet, May 16 2002

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