27672 is a member of OEIS A061317: split positive integers into extending even groups and sum: 1+2, 3+ ... +6, 7+ ... +12, 13+ ... +20, ... The sequence can be generated as follows:

INPUT

L=[]

number=1

for n in range(1,52,2):

  start=number

  number=number+n

  T=[x for x in [start..number]]

  L.append(sum(T))

  number+=1

print(L)

OUTPUT

[3, 18, 57, 132, 255, 438, 693, 1032, 1467, 2010, 2673, 3468, 4407, 5502, 6765, 8208, 9843, 11682, 13737, 16020, 18543, 21318, 24357, 27672, 31275, 35178]

27672 is a member of OEIS A356854: palindromes that can be written in more than one way as the sum of two distinct palindromic primes. Here the primes are:

[11311, 16361] and [13331, 14341]

The sequence can be generated as follows:

INPUT

L=[]

P=[p for p in prime_range(10,40000) if str(p)==str(p) [::-1]]

C=Combinations(P,2)

for c in C:

  if str(sum(c))==str(sum(c)) [::-1]:

    L.append(sum(c))

    if sum(c)==27672:

      print(c)

for n in L:

  if L.count(n)==1:

    L.remove(n)

print(sorted(L))

OUTPUT

[232, 282, 282, 414, 474, 484, 484, 666, 696, 808, 858, 858, 878, 888, 888, 20902, 21712, 21912, 21912, 22722, 22722, 23832, 23832, 24642, 24642, 24942, 25752, 25752, 25752, 25952, 26362, 26662, 26662, 26762, 26762, 26862, 26862, 26862, 26862, 26962, 26962, 26962, 27672, 27672, 27772, 27772, 27872, 27872, 27972, 27972, 27972, 27972, 28482, 28482, 28782, 28782, 28782, 28782, 28782, 28782, 28882, 28882, 28882, 28982, 28982, 29692, 29692, 29792, 29792, 29892, 29892, 29892, 29892, 29892, 29892, 29992, 29992, 29992, 40504, ...]

27672 is palindromic in base 10.

27672 is a Harshad number since it is a multiple of its sum of digits (24), and also a Moran number because the ratio is a prime number: 1153 = 27672 / (2 + 7 + 6 + 7 + 2).

27672 is an untouchable number because it is not equal to the sum of proper divisors of any number.

27672 is an abundant, Zumkeller and pseudoperfect number.

27672 is NOT unprimeable because 27673 is prime.

27672 requires 22 steps to reach a home prime.

27672 has an aliquot sequence that does not terminate after 101 steps.

27672 can be rendered as a digit equation as follows:

2 / (7 - 6) ^7 = 2