A366438 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

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.