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

1,2

Links

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

Formula

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

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 &]

Prog

(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, ", "))); }

Crossrefs

Cf. A268335, A322483, A368469.

Sequence in context: A029658 A332889 A239452 * A069930 A086327 A114896

Adjacent sequences: A368465 A368466 A368467 * A368469 A368470 A368471

Keyword

nonn,easy

Author

Amiram Eldar, Dec 26 2023

Status

approved