27320 is a number that is on the trajectory of 41 under the 17n+1 Collatz-like trajectory. The trajectory can be generated using the following algorithm:

INPUT

P={2,3,5,7,11,13}

n=41

L=[]

while n not in L:

  L.append(n)

  G=Set(prime_factors(n))

  if P.intersection(G)==set():

    n=17*n+1

  else:

    F=list(factor(n))

    for f in F:

      if f[0] in P:

        n=int(n/(f[0]^f[1]))

L.append(n)

print(L) 

OUTPUT

[41, 698, 349, 5934, 989, 16814, 1201, 20418, 3403, 57852, 1607, 27320, 683, 11612, 2903, 49352, 6169, 104874, 227, 3860, 193, 3282, 547, 9300, 31, 528, 1, 18, 1]

27320 is a junction number because it is equal to n + sod(n) for n = 27295 and 27304.

27320 is an abundant, pseudoperfect and Zumkeller number.