A366538 The number of unitary divisors of the exponentially 2^n-numbers (A138302).

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, 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, 8, 2, 4, 2, 4, 2, 8, 4, 4, 4, 2, 8, 4, 4, 4, 4, 4, 2, 4

Offset

1,2

Comments

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.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

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

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

Mathematica

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

Prog

(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, ", ")));

Crossrefs

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

Similar sequences: A366534, A366536.

Sequence in context: A069733 A187467 A081755 * A366536 A349355 A353589

Adjacent sequences: A366535 A366536 A366537 * A366539 A366540 A366541

Keyword

nonn,easy

Author

Amiram Eldar, Oct 12 2023

Status

approved