Search: id:A065704
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%I A065704
%S A065704 1,2,1,3,1,2,1,4,2,2,1,3,1,2,1,5,1,4,1,3,1,2,1,4,2,2,2,3,1,2,1,6,1,2,1,
%T A065704 6,1,2,1,4,1,2,1,3,2,2,1,5,2,4,1,3,1,4,1,4,1,2,1,3,1,2,2,7,1,2,1,3,1,2,
%U A065704 1,8,1,2,2,3,1,2,1,5,3,2,1,3,1,2,1,4,1,4,1,3,1,2,1,6,1,4,2,6,1,2,1,4,1
%N A065704 Number or squares or twice squares dividing n.
%F A065704 1/2*Sum_{ d divides n } (1-(-1)^sigma(d)). Multiplicative with a(2^e) 
               = e+1 and a(p^e) = floor(e/2)+1 for an odd prime p.
%e A065704 divisors(36) = {1, 2, 3, 4, 6, 9, 12, 18, 36}, thus a(36) = #{1, 2, 4, 
               9, 18, 36}=6. a(36) = 1/2*(tau(36)-((-1)^sigma(1)+(-1)^sigma(2)+(-1)^sigma(3)+(-1)^sigma(4)+(-1)^sigma(6)\
               +(-1)^sigma(9)+(-1)^sigma(12)+(-1)^sigma(18)+(-1)^sigma(36))) = 1/
               2*(9-(-3)) = 6. a(36) = a(2^2*3^2) = a(2^2)*a(3^2) = (2+1)*(1+1) 
               = 6.
%Y A065704 Cf. A000203, A028982, A046951.
%Y A065704 Sequence in context: A156249 A164677 A001511 this_sequence A026100 A059127 
               A105609
%Y A065704 Adjacent sequences: A065701 A065702 A065703 this_sequence A065705 A065706 
               A065707
%K A065704 mult,nonn
%O A065704 1,2
%A A065704 Vladeta Jovovic (vladeta(AT)eunet.rs), Dec 04 2001
%E A065704 More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Sep 09 
               2002

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