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%I #8 May 12 2022 19:32:54
%S 1,1,1,5,1,1,1,13,10,1,1,17,1,1,16,29,1,10,1,25,22,1,1,49,26,1,10,33,
%T 1,16,1,61,34,1,36,62,1,1,40,73,1,22,1,49,25,1,1,113,50,26,52,57,1,10,
%U 56,97,58,1,1,112,1,1,31,125,66,34,1,73,70,36,1,166,1,1,41,81,78
%N Sum of the divisors of n whose arithmetic derivative is even.
%F a(n) = Sum_{d|n} d * ((1+d') mod 2).
%t d[1] = 0; d[n_] := n * Plus @@ ((Last[#]/First[#]) & /@ FactorInteger[n]); a[n_] := DivisorSum[n, # &, EvenQ[d[#]] &]; Array[a, 100] (* _Amiram Eldar_, May 12 2022 *)
%o (PARI) ad(n) = vecsum([n/f[1]*f[2]|f<-factor(n+!n)~]); \\ A003415
%o a(n) = sumdiv(n, d, if (!(ad(d) % 2), d)); \\ _Michel Marcus_, May 12 2022
%Y Cf. A000005 (tau), A003415 (n').
%K nonn
%O 1,4
%A _Wesley Ivan Hurt_, May 12 2022