27643 is a member of OEIS A064125: numbers k such that k and k+1 have the same sum of unitary divisors, here 34560. The sequence can be generated as follows:

INPUT

L=[]

for n in [1..40000]:

  total1 = 0

  D = divisors(n)

  for i in range(0, len(D)):

    if gcd(D[i], n/D[i]) == 1:

      total1 = total1+D[i]

  if n==27643:

    print(n,"has unitary divisors of",D,"with sum",total1)

  total2 = 0

  D = divisors(n+1)

  for i in range(0,len(D)):

    if gcd(D[i],(n+1)/D[i]) == 1:

      total2 =total2+D[i]

  if n==27643:

    print(n+1,"has unitary divisors of",D,"with sum",total2)

  if total1==total2:

    L.append(n)

print(L)

OUTPUT

27643 has unitary divisors of [1, 7, 11, 77, 359, 2513, 3949, 27643] with sum 34560

27644 has unitary divisors of [1, 2, 4, 6911, 13822, 27644] with sum 34560

[14, 44, 55, 152, 957, 1334, 1400, 1634, 1652, 2204, 2232, 2295, 2685, 3195, 3451, 3956, 4256, 5547, 7191, 8216, 8495, 8636, 8907, 9144, 9503, 9844, 10152, 11515, 17255, 18423, 19491, 20145, 20155, 27404, 27643, 30247, 33998, 38180]

27643 is a sphenic, Duffinian and cyclic number; nialpdrome in base 13 (c775).

27643 can be rendered as a digital equation as follows:

-2 + 7 = 6 - 4 + 3