27674 is a product of 2 and two 4k+1 primes and so it can be expressed as a sum of two squares in two different ways viz. 55^2+157^2 and 85^2+143^2.

27674 is a sphenic numbers whose three prime factors all have the same digital root, here 2.

There are 111 such numbers in the range up to 40000. The first is 638 = 2 * 11 * 29 where each factor has a digital root of 2.

L=[]

for n in [1..40000]:

  if len(divisors(n))==8 and len(prime_factors(n))==3:

    P=prime_factors(n)

    b=10

    DR=[0,0,0]

    for i in [0..2]:

      if sum(P[i].digits(b))%(b-1)!=0:

        DR[i]=sum(P[i].digits())%(b-1)

      else:

        DR[i]=9

    if DR[0]==DR[1] and DR[1]==DR[2]:

      L.append(n)

print(L)

print(len(L))

[638, 1034, 1826, 2222, 2726, 3014, 3806, 4202, 4715, 4814, 4994, 5786, 5858, 6182, 6785, 6974, 7766, 7802, 7946, 8558, 9494, 9746, 10034, 10142, 10538, 11078, 12095, 12518, 12878, 12914, 12995, 13166, 14102, 14498, 14894, 14993, 15065, 15254, 16262, 16298, 16766, 17135, 17954, 18062, 18361, 18386, 18458, 18854, 19205, 20042, 20438, 20474, 20834, 21338, 21626, 22418, 22562, 22742, 23165, 23779, 24002, 24398, 24722, 25586, 25694, 25982, 26414, 26477, 26738, 26774, 26855, 27001, 27485, 27674, 27782, 28358, 28718, 28754, 29197, 29555, 29798, 29942, 30545, 31526, 31706, 31922, 32219, 32714, 33002, 33182, 33335, 33506, 33695, 33733, 34046, 34235, 34298, 34946, 35486, 35765, 36566, 36674, 37178, 37682, 37862, 38222, 38582, 38645, 39266, 39842, 39905]

111

27674 can be rendered as a digit equation as follows:

-2 + 7 + 6 = 7 + 4