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A111371
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A number k is included if at least one prime dividing k is equal to an exponent of the highest power of any prime dividing k.
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2
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4, 12, 18, 20, 24, 27, 28, 36, 44, 50, 52, 54, 60, 68, 72, 76, 84, 90, 92, 98, 100, 108, 116, 120, 124, 126, 132, 135, 140, 144, 148, 150, 156, 160, 164, 168, 172, 180, 188, 189, 196, 198, 200, 204, 212, 216, 220, 228, 234, 236, 242, 244, 252, 260, 264, 268, 270
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OFFSET
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1,1
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COMMENTS
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The number of terms not exceeding 10^m, for m = 1, 2, ..., are 1, 21, 216, 2186, 21921, 219274, 2192979, 21930103, 219301557, 2193017386, ... . Apparently, the asymptotic density of this sequence exists and equals 0.21930... . - Amiram Eldar, Jun 24 2022
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LINKS
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EXAMPLE
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50 = 2^1 * 5^2. 2 is both a prime dividing 50 and the exponent of the highest power of 5 dividing 50. So 50 is in the sequence.
144 = 2^4 * 3^2. 2 is a prime dividing 144 and the exponent of the highest power of 3 dividing 144. So 144 is in the sequence.
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MATHEMATICA
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Select[Range[2, 300], Intersection @@ Transpose[FactorInteger[ # ]] != {} &] (* Ray Chandler, Nov 09 2005 *)
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PROG
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(Python)
from sympy import factorint
def aupto(limit):
alst = []
for k in range(4, limit+1):
f = factorint(k)
# if max(f[p] for p in f) in f: alst.append(k)
if set(f[p] for p in f) & set(f) != set(): alst.append(k)
return alst
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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