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%I A007421 M0067 #39 May 19 2020 07:13:24
%S A007421 2,1,1,2,1,2,1,1,2,2,1,1,1,2,2,2,1,1,1,1,2,2,1,2,2,2,1,1,1,1,1,1,2,2,
%T A007421 2,2,1,2,2,2,1,1,1,1,1,2,1,1,2,1,2,1,1,2,2,2,2,2,1,2,1,2,1,2,2,1,1,1,
%U A007421 2,1,1,1,1,2,1,1,2,1,1,1,2,2,1,2,2,2,2,2,1,2,2,1,2,2,2,2,1,1,1,2,1,1,1,2,1
%N A007421 Liouville's function: parity of number of primes dividing n (with multiplicity).
%D A007421 J. Roberts, Lure of the Integers, Math. Assoc. America, 1992, p. 279.
%D A007421 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A007421 Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
%H A007421 H. Gupta, On a table of values of L(n), Proceedings of the Indian Academy of Sciences. Section A, 12 (1940), 407-409. [Annotated scanned copy]
%H A007421 R. S. Lehman, On Liouville's function, Math. Comp., 14 (1960), 311-320.
%F A007421 a(n) = ((-1)^bigomega(n)+3)/2, where bigomega(n) is the number of prime divisors of the integer n counted with multiplicity.
%F A007421 a(n) = A065043(n) + 1.
%F A007421 a(n) = 2 - A001222(n) mod 2. - _Reinhard Zumkeller_, Nov 10 2011
%t A007421 a[1] = 2; a[n_] := ((-1)^Total[FactorInteger[n][[All, 2]]] + 3)/2; (* or, from version 7 on : *) a[n_] := Boole[ EvenQ[ PrimeOmega[n]]] + 1; (* or *) a[n_] := (LiouvilleLambda[n] + 3)/2; a[1] = 2; Table[a[n], {n, 1, 105}] (* _Jean-François Alcover_, Apr 08 2013, updated Jan 27 2015 *)
%o A007421 (Haskell)
%o A007421 a007421 = (2 -) . (`mod` 2) . a001222 -- _Reinhard Zumkeller_, Nov 10 2011
%Y A007421 Cf. A008836, A065043.
%K A007421 nonn,easy,nice
%O A007421 1,1
%A A007421 _N. J. A. Sloane_
%E A007421 More terms from _Vladeta Jovovic_, Dec 01 2001
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