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The number of unitary divisors of the exponentially odd numbers (A268335).
6

%I #10 Oct 12 2023 09:51:52

%S 1,2,2,2,4,2,2,4,2,2,4,4,2,2,4,4,2,4,4,2,2,8,2,2,4,4,4,2,4,4,4,2,8,2,

%T 4,2,4,2,4,4,4,4,4,2,2,4,4,8,2,4,8,2,2,4,4,8,2,4,2,4,4,4,4,2,4,4,4,4,

%U 4,2,2,8,2,4,8,4,2,2,8,4,2,8,4,4,4,8,4

%N The number of unitary divisors of the exponentially odd numbers (A268335).

%H Amiram Eldar, <a href="/A366534/b366534.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A034444(A268335(n)).

%t f[n_] := Module[{e = FactorInteger[n][[;; , 2]]}, If[AllTrue[e, OddQ], 2^Length[e], Nothing]]; f[1] = 1; Array[f, 150]

%o (PARI) lista(max) = for(k = 1, max, my(e = factor(k)[, 2], isexpodd = 1); for(i = 1, #e, if(!(e[i] % 2), isexpodd = 0; break)); if(isexpodd, print1(2^(#e), ", ")));

%Y Cf. A034444, A077610, A268335, A366438, A366535.

%Y Similar sequences: A366536, A366538.

%K nonn,easy

%O 1,2

%A _Amiram Eldar_, Oct 12 2023