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

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, 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, 8, 2, 2, 8, 2, 6, 8, 4, 2, 2, 8, 4, 2, 8, 4, 4, 4, 12, 4

Offset: 1

Author

Amiram Eldar, Dec 26 2023

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A268335, A322483, A368469.

Programs

Mathematica

f[p_, e_] := (e + 3)/2; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; s /@ Select[Range[200], AllTrue[FactorInteger[#][[;; , 2]], OddQ] &]
(* or *)
f[p_, e_] := If[OddQ[e], (e + 3)/2, 0]; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; Select[Array[s, 200], # > 0 &]

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, ", ")));}

Formula

a(n) = A322483(A268335(n)).