27312 is a member of OEIS A255215: numbers that belong to at least one amicable tuple, here (27312, 21168, 22200). The tuples are easy to find once one member is identified but otherwise, to find all the members of this sequence is very processor intensive.

INPUT

number=27312

L=[number]

for n in [1..40000]:

  if sigma(n)==sigma(number) and n != number:

    L.append(n)

print(L)

C=Combinations(L,3)

for c in C:

  if sum(c)==sigma(number):

    print(c,sum(c))

OUTPUT

[27312, 21168, 22200, 30200, 30320, 33075, 34352, 34928, 35150]

[27312, 21168, 22200] 70680

27312 is a junction number because it is equal to n+sod(n) for n = 27291 and 27300.

27312 is a member of OEIS A331824: starts of runs of FOUR consecutive positive negabinary-Niven numbers (A331728). See blog post Negabinary Niven Numbers.

The initial members of the sequence are:

1, 1264, 2104, 2944, 4624, 11888, 23768, 27312, 27728, 31688, 35648, ...

27312 is an abundant, pseudoperfect and Zumkeller number.