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A323399 Sum of Jordan function J_2(n), A007434 and its Dirichlet inverse, A046970.

%I A323399 #7 Jan 13 2019 19:29:54
%S A323399 2,0,0,9,0,48,0,45,64,144,0,120,0,288,384,189,0,240,0,360,768,720,0,
%T A323399 408,576,1008,640,720,0,0,0,765,1920,1728,2304,888,0,2160,2688,1224,0,
%U A323399 0,0,1800,1920,3168,0,1560,2304,1872,4608,2520,0,1968,5760,2448,5760,5040,0,1728,0,5760,3840,3069,8064,0,0,4320,8448,0,0,3480,0,8208,4992,5400
%N A323399 Sum of Jordan function J_2(n), A007434 and its Dirichlet inverse, A046970.
%H A323399 Antti Karttunen, <a href="/A323399/b323399.txt">Table of n, a(n) for n = 1..16384</a>
%F A323399 a(n) = A007434(n) + A046970(n).
%o A323399 (PARI)
%o A323399 A007434(n) = sumdiv(n, d, d*d*moebius(n/d));
%o A323399 A046970(n) = if(1==n,n,my(f=factor(n)); for(i=1, #f~, f[i,1] = 1-(f[i,1]^2)); factorback(f[,1]));
%o A323399 A323399(n) = (A007434(n) + A046970(n));
%Y A323399 Cf. A007434, A046970.
%Y A323399 Cf. also A319340, A322581, A323364.
%K A323399 nonn
%O A323399 1,1
%A A323399 _Antti Karttunen_, Jan 13 2019