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A104210
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Positive integers divisible by at least 2 consecutive primes.
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10
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6, 12, 15, 18, 24, 30, 35, 36, 42, 45, 48, 54, 60, 66, 70, 72, 75, 77, 78, 84, 90, 96, 102, 105, 108, 114, 120, 126, 132, 135, 138, 140, 143, 144, 150, 154, 156, 162, 165, 168, 174, 175, 180, 186, 192, 195, 198, 204, 210, 216, 221, 222, 225, 228, 231, 234, 240
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OFFSET
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1,1
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COMMENTS
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If a perfect square is in this sequence, then so is its square root (e.g., 144 and 12). - Alonso del Arte, May 07 2012
The numbers of terms not exceeding 10^k, for k=1,2,..., are 1, 22, 242, 2456, 24632, 246414, 2464272, 24643281, 246433426, ... Apparently, the asymptotic density of this sequence is 0.24643... - Amiram Eldar, Apr 10 2021
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LINKS
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EXAMPLE
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35 is divisible by both 5 and 7, and 5 and 7 are consecutive primes.
77 is divisible by both 7 and 11, and 7 and 11 are consecutive primes.
110 is not in the sequence because, although it is divisible by 2, 5 and 11, it is not divisible by 3 or 7.
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MAPLE
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N:= 1000: # for terms <= N
R:= {}:
p:= 2:
do
q:= p; p:= nextprime(p);
if p*q > N then break fi;
R:= R union {seq(i, i=p*q..N, p*q)}
od:
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MATHEMATICA
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fQ[n_] := Block[{lst = PrimePi /@ Flatten[ Table[ #[[1]], {1}] & /@ FactorInteger[n]]}, Count[ Drop[lst, 1] - Drop[lst, -1], 1] > 0]; Select[ Range[244], fQ[ # ] &] (* Robert G. Wilson v, Mar 16 2005 *)
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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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