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A104210
Positive integers divisible by at least 2 consecutive primes.
12
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
OFFSET
1,1
COMMENTS
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
LINKS
EXAMPLE
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.
MAPLE
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:
sort(convert(R, list)); # Robert Israel, Apr 13 2020
MATHEMATICA
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 *)
CROSSREFS
Sequence in context: A315616 A091011 A324771 * A356736 A066312 A309944
KEYWORD
nonn
AUTHOR
Leroy Quet, Mar 13 2005
EXTENSIONS
More terms from Robert G. Wilson v, Mar 16 2005
STATUS
approved