A366438 The number of divisors of the exponentially odd numbers (A268335).

1, 2, 2, 2, 4, 2, 4, 4, 2, 2, 4, 4, 2, 2, 4, 4, 2, 8, 4, 4, 2, 8, 2, 6, 4, 4, 4, 2, 4, 4, 8, 2, 8, 2, 4, 2, 4, 2, 8, 4, 8, 4, 4, 2, 2, 4, 4, 8, 2, 4, 8, 2, 2, 4, 4, 8, 2, 4, 2, 4, 4, 4, 8, 2, 4, 4, 4, 4, 12, 2, 2, 8, 2, 8, 8, 4, 2, 2, 8, 4, 2, 8, 4, 4, 4, 16, 4

Offset

1,2

Comments

1 is the only odd term in this sequence.

Links

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

Formula

a(n) = A000005(A268335(n)).

Mathematica

f[n_] := Module[{e = FactorInteger[n][[;; , 2]]}, If[AllTrue[e, OddQ], Times @@ (e + 1), Nothing]]; f[1] = 1; Array[f, 150]

Prog

(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(vecprod(apply(x -> x+1, e)), ", ")));
(Python)
from math import prod
from itertools import count, islice
from sympy import factorint
def A366438_gen(): # generator of terms
    for n in count(1):
        f = factorint(n).values()
        if all(e&1 for e in f):
            yield prod(e+1 for e in f)
A366438_list = list(islice(A366438_gen(), 30)) # Chai Wah Wu, Oct 10 2023

Crossrefs

Cf. A000005, A268335, A366439.

Similar sequences: A048691, A072048, A076400, A358040, A363194, A363195.

Sequence in context: A161841 A335901 A372468 * A152674 A072056 A356831

Adjacent sequences: A366435 A366436 A366437 * A366439 A366440 A366441

Keyword

nonn,easy

Author

Amiram Eldar, Oct 10 2023

Status

approved