Search: id:A046660
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%I A046660
%S A046660 0,0,0,1,0,0,0,2,1,0,0,1,0,0,0,3,0,1,0,1,0,0,0,2,1,0,2,1,0,0,0,4,0,0,0,
               2,0,
%T A046660 0,0,2,0,0,0,1,1,0,0,3,1,1,0,1,0,2,0,2,0,0,0,1,0,0,1,5,0,0,0,1,0,0,0,3,
               0,0,
%U A046660 1,1,0,0,0,3,3,0,0,1,0,0,0,2,0,1,0,1,0,0,0,4,0,1,1,2,0,0,0,2,0,0,0,3,0,
               0,0
%N A046660 Excess of n = number of primes divisors (with multiplicity) - number 
               of prime divisors (without multiplicity).
%C A046660 a(n) depends only on prime signature of n (cf. A025487). So a(24) = a(375) 
               since 24=2^3*3 and 375=3*5^3 both have prime signature (3,1).
%C A046660 a(n) = 0 for square-free n.
%C A046660 A162511(n) = (-1)^a(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Jul 08 2009]
%D A046660 M. Kac, Statistical Independence in Probability, Analysis and Number 
               Theory, Carus Monograph 12, Math. Assoc. Amer., 1959, see p. 64.
%F A046660 a(n) = Omega(n) - omega(n) = A001222(n) - A001221(n).
%F A046660 Additive with a(p^e) = e - 1.
%Y A046660 Cf. A001222, A001221. Not the same as A066301.
%Y A046660 Sequence in context: A081221 A103840 A066301 this_sequence A108730 A056973 
               A107782
%Y A046660 Adjacent sequences: A046657 A046658 A046659 this_sequence A046661 A046662 
               A046663
%K A046660 nonn,easy,nice
%O A046660 1,8
%A A046660 N. J. A. Sloane (njas(AT)research.att.com).
%E A046660 More terms from David W. Wilson (davidwwilson(AT)comcast.net).

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