%I #11 May 13 2022 09:53:11
%S 1,2,3,2,5,36,7,2,3,100,11,36,13,196,15,2,17,648,19,100,21,484,23,36,
%T 5,676,81,196,29,54000,31,2,33,1156,35,648,37,1444,39,100,41,148176,
%U 43,484,675,2116,47,36,7,5000,51,676,53,944784,55,196,57,3364,59,54000,61,3844
%N Product of the divisors of n whose arithmetic derivative is odd.
%F a(n) = Product_{d|n} d^((d') mod 2), where d' is the arithmetic derivative of d.
%e a(6) = 36; the product of the divisors of 6 whose arithmetic derivative is odd is 2*3*6 = 36.
%t d[1] = 0; d[n_] := n*Plus @@ ((Last[#]/First[#]) & /@ FactorInteger[n]); a[n_] := Product[k^Mod[d[k], 2], {k, Divisors[n]}]; Array[a, 60] (* _Amiram Eldar_, May 13 2022 *)
%o (PARI) ad(n) = vecsum([n/f[1]*f[2]|f<-factor(n+!n)~]); \\ A003415
%o a(n) = vecprod(select(x->(ad(x) % 2), divisors(n))); \\ _Michel Marcus_, May 13 2022
%Y Cf. A003415 (n'), A353976.
%K nonn
%O 1,2
%A _Wesley Ivan Hurt_, May 12 2022