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A368468 a(n) is the number of exponentially odd divisors of the n-th exponentially odd number.

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%I A368468 #8 Dec 27 2023 01:22:36
%S A368468 1,2,2,2,4,2,3,4,2,2,4,4,2,2,4,4,2,6,4,3,2,8,2,4,4,4,4,2,4,4,6,2,8,2,
%T A368468 4,2,4,2,6,4,6,4,4,2,2,4,4,8,2,4,8,2,2,4,4,8,2,4,2,4,4,4,6,2,4,4,4,4,
%U A368468 8,2,2,8,2,6,8,4,2,2,8,4,2,8,4,4,4,12,4
%N A368468 a(n) is the number of exponentially odd divisors of the n-th exponentially odd number.
%H A368468 Amiram Eldar, <a href="/A368468/b368468.txt">Table of n, a(n) for n = 1..10000</a>
%F A368468 a(n) = A322483(A268335(n)).
%t A368468 f[p_, e_] := (e + 3)/2; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; s /@ Select[Range[200], AllTrue[FactorInteger[#][[;; , 2]], OddQ] &]
%t A368468 (* or *)
%t A368468 f[p_, e_] := If[OddQ[e], (e + 3)/2, 0]; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; Select[Array[s, 200], # > 0 &]
%o A368468 (PARI) lista(kmax) = {my(e, d); for(k = 1, kmax, e = factor(k)[, 2]; d = prod(i = 1, #e, if(e[i]%2, (e[i] + 3)/2, 0)); if(d > 0, print1(d, ", ")));}
%Y A368468 Cf. A268335, A322483, A368469.
%K A368468 nonn,easy
%O A368468 1,2
%A A368468 _Amiram Eldar_, Dec 26 2023