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A366438
The number of divisors of the exponentially odd numbers (A268335).
8
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
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
Similar sequences: A048691, A072048, A076400, A358040, A363194, A363195.
Sequence in context: A161841 A335901 A372468 * A152674 A072056 A356831
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Oct 10 2023
STATUS
approved