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A349342 Sum of A026741 and its Dirichlet inverse.

%I A349342 #10 Nov 21 2021 10:16:07
%S A349342 2,0,0,1,0,6,0,3,9,10,0,9,0,14,30,7,0,9,0,15,42,22,0,15,25,26,27,21,0,
%T A349342 0,0,15,66,34,70,18,0,38,78,25,0,0,0,33,45,46,0,27,49,25,102,39,0,27,
%U A349342 110,35,114,58,0,15,0,62,63,31,130,0,0,51,138,0,0,36,0,74,75,57,154,0,0,45,81,82,0,21,170,86
%N A349342 Sum of A026741 and its Dirichlet inverse.
%H A349342 Antti Karttunen, <a href="/A349342/b349342.txt">Table of n, a(n) for n = 1..20000</a>
%F A349342 a(n) = A026741(n) + A349341(n).
%F A349342 a(1) = 2, and for n > 1, a(n) = -Sum_{d|n, 1<d<n} A026741(d) * A349341(n/d).
%o A349342 (PARI)
%o A349342 A026741(n) = if(n%2,n,n/2);
%o A349342 A349341(n) = { my(f = factor(n)); prod(i=1, #f~, if(2==f[i,1], -1, if(1==f[i,2], -f[i,1], 0))); };
%o A349342 A349342(n) = (A026741(n)+A349341(n));
%Y A349342 Cf. A026741, A349341.
%K A349342 nonn
%O A349342 1,1
%A A349342 _Antti Karttunen_, Nov 15 2021