A366538 - OEIS

%I #7 Oct 12 2023 09:51:43

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

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

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

%N The number of unitary divisors of the exponentially 2^n-numbers (A138302).

%C Also, the number of infinitary divisors of the terms of A138302, since A138302 is also the sequence of numbers whose sets of unitary divisors (A077610) and infinitary divisors (A077609) coincide.

%H Amiram Eldar, <a href="/A366538/b366538.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A034444(A138302(n)).	

%F a(n) = A037445(A138302(n)).

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

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

%Y Cf. A034444, A037445, A077609, A077610, A138302, A366539.

%Y Similar sequences: A366534, A366536.

%K nonn,easy

%O 1,2

%A _Amiram Eldar_, Oct 12 2023