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%I #10 Jun 08 2022 16:28:51
%S 0,2,3,6,5,5,7,6,3,7,11,9,13,9,8,6,17,14,19,11,10,13,23,17,5,15,30,13,
%T 29,16,31,22,14,19,12,18,37,21,16,11,41,12,43,17,8,25,47,29,7,32,20,
%U 19,53,41,16,13,22,31,59,20,61,33,10,22,18,16,67,23,26,24,71,26,73
%N Sum of the nontrivial divisors of n whose arithmetic derivative divides n.
%F a(n) = Sum_{d|n, d'|n, d>1} d, where d' is the arithmetic derivative of d.
%e The sum of the nontrivial divisors of 6 whose arithmetic derivative divides 6 is 2 + 3 = 5.
%t d[1] = 0; d[n_] := n*Plus @@ ((Last[#]/First[#]) & /@ FactorInteger[n]); a[n_] := DivisorSum[n, # &, # > 1 && Divisible[n, d[#]] &]; Array[a, 100] (* _Amiram Eldar_, May 13 2022 *)
%o (PARI) ad(n) = vecsum([n/f[1]*f[2]|f<-factor(n+!n)~]); \\ A003415
%o a(n) = sumdiv(n, d, if ((d>1) && !(n % ad(d)), d)); \\ _Michel Marcus_, May 13 2022
%Y Cf. A003415, A323880.
%K nonn
%O 1,2
%A _Wesley Ivan Hurt_, May 12 2022