27324 is the lesser of a pair of adjacent composite numbers s.t. both are only one step away from their home primes (223331123 and 551093 respectively). See Bespoken for Sequences entry.

27324 is a happy, Harshad, practical, abundant, pseudoperfect and Zumkeller number.

27324 is a junction number because it is equal to n + sod(n) for n = 27297 and 27306.

27324 is a d-powerful number because it can be written as 2^9 + 7^2 + 3^7 + 2^13 + 4^7 .

27324 is a number whose prime factors contain only the digits 1, 2 or 3. See Bespoken for Sequences entry. There are 1295 such numbers in the range up to 40,000. Here are the numbers from 27234 to 40,000:

27324, 27346, 27368, 27378, 27443, 27456, 27459, 27469, 27508, 27544, 27621, 27641, 27648, 27652, 27703, 27732, 27807, 27852, 27899, 27996, 28024, 28089, 28129, 28193, 28296, 28313, 28314, 28431, 28512, 28544, 28561, 28566, 28589, 28612, 28704, 28769, 28796, 28873, 28892, 28923, 28928, 28989, 29016, 29062, 29109, 29112, 29118, 29128, 29198, 29213, 29282, 29352, 29403, 29436, 29544, 29601, 29606, 29744, 29791, 29808, 29817, 29824, 29832, 29856, 29907, 29952, 29979, 30008, 30043, 30048, 30132, 30173, 30321, 30329, 30383, 30384, 30452, 30523, 30613, 30654, 30752, 30756, 30774, 30783, 30789, 30888, 30976, 30987, 31096, 31104, 31188, 31372, 31434, 31527, 31538, 31702, 31704, 31713, 31744, 31776, 31798, 31833, 31889, 31944, 32006, 32076, 32112, 32154, 32292, 32318, 32344, 32384, 32448, 32488, 32544, 32552, 32643, 32736, 32751, 32768, 32769, 32798, 32916, 33021, 33143, 33237, 33319, 33339, 33393, 33396, 33462, 33534, 33536, 33552, 33561, 33588, 33639, 33696, 33759, 33776, 33787, 33792, 33804, 33808, 33856, 33933, 33963, 34096, 34182, 34224, 34322, 34331, 34346, 34424, 34584, 34596, 34606, 34749, 34788, 34813, 34848, 34914, 34983, 34992, 35143, 35152, 35256, 35328, 35369, 35408, 35431, 35464, 35536, 35659, 35667, 35712, 35748, 35936, 35937, 36126, 36156, 36179, 36339, 36348, 36387, 36432, 36443, 36501, 36504, 36549, 36553, 36608, 36612, 36621, 36633, 36641, 36828, 36864, 36969, 36976, 37059, 37076, 37136, 37328, 37403, 37452, 37466, 37479, 37603, 37631, 37687, 37728, 37746, 37752, 37873, 37908, 37913, 37998, 38016, 38034, 38088, 38161, 38194, 38272, 38307, 38358, 38502, 38533, 38564, 38652, 38688, 38727, 38812, 38816, 38824, 38907, 39136, 39169, 39204, 39246, 39248, 39363, 39366, 39377, 39392, 39468, 39546, 39663, 39744, 39756, 39776, 39808, 39834, 39876, 39897, 39936, 39939, 39972, 39978, 39993]

27324 is a member of OEIS A046308: numbers that are divisible by exactly 7 primes counting multiplicity. There are 1089 such numbers in the range up 40,000. The number of prime factors with multiplicity can be found using the following:

INPUT

a = sloane.A001222

a(27324)

OUTPUT

7

The OEIS sequence can be generated as follows:

INPUT

L=[]

for n in [1..40000]:

  if is_prime(n)==0:

    F=list(factor(n))

    count=0

    for f in F:

      count+=f[1]

    if count==7:

      L.append(n)

print(L)

print(len(L))

OUTPUT (only from 27324 to 40000)

[... 27324, 27378, 27432, 27500, 27504, 27584, 27664, 27680, 27712, 27783, 27792, 27808, 27872, 27888, 27900, 27945, 27972, 27984, 28096, 28125, 28128, 28152, 28200, 28272, 28296, 28336, 28352, 28368, 28392, 28400, 28440, 28448, 28500, 28576, 28600, 28620, 28640, 28656, 28674, 28736, 28768, 28812, 28832, 28836, 28880, 28917, 28960, 28980, 29000, 29008, 29016, 29106, 29200, 29216, 29248, 29250, 29304, 29328, 29344, 29403, 29472, 29504, 29536, 29592, 29632, 29640, 29646, 29680, 29736, 29744, 29856, 29880, 29888, 29889, 29904, 29970, 29988, 30024, 30048, 30160, 30176, 30184, 30192, 30294, 30360, 30368, 30384, 30420, 30432, 30480, 30492, 30560, 30656, 30688, 30744, 30752, 30870, 30880, 30996, 31000, 31050, 31080, 31136, 31152, 31168, 31185, 31212, 31250, 31280, 31328, 31347, 31416, 31424, 31428, 31440, 31464, 31520, 31600, 31648, 31776, 31800, 31840, 31860, 31936, 31944, 32016, 32040, 32096, 32112, 32130, 32144, 32184, 32192, 32200, 32208, 32224, 32240, 32292, 32319, 32340, 32352, 32368, 32472, 32500, 32508, 32560, 32562, 32576, 32592, 32616, 32670, 32688, 32724, 32864, 32880, 32886, 32912, 32940, 32976, 33040, 33072, 33075, 33184, 33200, 33210, 33300, 33312, 33320, 33344, 33360, 33372, 33376, 33456, 33472, 33488, 33504, 33516, 33552, 33660, 33712, 33744, 33760, 33768, 33800, 33824, 33858, 33880, 33888, 33912, 33936, 34056, 34104, 34144, 34160, 34224, 34263, 34300, 34336, 34398, 34416, 34425, 34440, 34452, 34464, 34500, 34506, 34528, 34592, 34608, 34624, 34632, 34650, 34668, 34680, 34704, 34749, 34830, 34884, 34920, 34960, 35008, 35088, 35112, 35152, 35154, 35168, 35208, 35232, 35235, 35316, 35376, 35400, 35478, 35496, 35532, 35552, 35600, 35648, 35672, 35680, 35700, 35728, 35760, 35784, 35802, 35808, 35872, 35880, 35910, 35952, 36032, 36036, 36072, 36080, 36120, 36144, 36176, 36180, 36240, 36256, 36300, 36320, 36360, 36384, 36416, 36448, 36456, 36512, 36540, 36544, 36600, 36612, 36624, 36640, 36704, 36750, 36768, 36784, 36792, 36816, 36828, 36848, 36855, 36900, 36928, 37000, 37008, 37024, 37080, 37088, 37125, 37128, 37224, 37240, 37280, 37344, 37368, 37392, 37400, 37408, 37488, 37520, 37568, 37620, 37664, 37665, 37680, 37752, 37840, 37872, 37944, 37952, 37968, 38048, 38064, 38070, 38088, 38112, 38192, 38220, 38240, 38250, 38280, 38336, 38340, 38352, 38368, 38376, 38394, 38464, 38475, 38480, 38496, 38500, 38520, 38544, 38560, 38610, 38624, 38637, 38664, 38700, 38736, 38752, 38760, 38800, 38848, 38896, 38988, 39008, 39024, 39060, 39096, 39120, 39123, 39150, 39216, 39232, 39240, 39264, 39375, 39420, 39440, 39480, 39488, 39616, 39672, 39712, 39760, 39776, 39780, 39816, 39888, 39900, 39904]

1089