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%I #13 Dec 07 2021 20:13:28
%S 0,0,0,4,0,1,0,20,5,1,0,37,0,6,12,100,0,16,0,49,7,1,0,101,7,8,32,90,0,
%T 15,0,276,9,1,16,144,0,10,32,137,0,15,0,117,33,10,0,421,9,47,24,104,0,
%U 151,32,202,13,1,0,191,0,14,32,916,21,12,0,161,15,24,0,428,0,16,35
%N a(n) = Sum_{d|n} d'', where d'' is the second arithmetic derivative of d (A068346).
%C Sum of the 2nd arithmetic derivatives of the divisors of n.
%H Antti Karttunen, <a href="/A348304/b348304.txt">Table of n, a(n) for n = 1..20000</a>
%F a(p) = 0 for primes p, since we have 1'' + p'' = 0' + 1' = 0 + 0 = 0.
%F a(n) = Sum_{d|n} A068346(d). - _Antti Karttunen_, Dec 07 2021
%e a(8) = 20; a(8) = 1'' + 2'' + 4'' + 8'' = 0 + 0 + 4 + 16 = 20.
%o (PARI) ad(n) = vecsum([n/f[1]*f[2]|f<-factor(n+!n)~]); \\ A003415
%o a(n) = sumdiv(n, d, ad(ad(d))); \\ _Michel Marcus_, Oct 11 2021
%Y Inverse Möbius transform of A068346 (2nd arithmetic derivative).
%Y Cf. A319684, A348279.
%K nonn,look
%O 1,4
%A _Wesley Ivan Hurt_, Oct 10 2021
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