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A215217
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Smaller member of a pair of sphenic twins, consecutive integers, each the product of three distinct primes.
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10
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230, 285, 429, 434, 609, 645, 741, 805, 902, 969, 986, 1001, 1022, 1065, 1085, 1105, 1130, 1221, 1245, 1265, 1309, 1310, 1334, 1406, 1434, 1442, 1462, 1490, 1505, 1533, 1581, 1598, 1605, 1614, 1634, 1729, 1742, 1833, 1885, 1886, 1946, 2013, 2014, 2054, 2085
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OFFSET
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1,1
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COMMENTS
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455 is not a term of the sequence, since 455 = 5*7*13 is sphenic, i.e., the number of distinct prime factors is 3, though 456 = 2^3*3*19 has 3 distinct prime factors but is not sphenic, because the number of prime factors with repetition is 5 > 3.
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LINKS
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MAPLE
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Sphenics:= select(t -> (map(s->s[2], ifactors(t)[2])=[1, 1, 1]), {$1..10000}):
Sphenics intersect map(`-`, Sphenics, 1); # Robert Israel, Aug 13 2014
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MATHEMATICA
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Select[Range[2500], (PrimeNu[#] == PrimeOmega[#] == PrimeNu[#+1] == PrimeOmega[#+1] == 3)&] (* Jean-François Alcover, Apr 11 2014 *)
SequencePosition[Table[If[PrimeNu[n]==PrimeOmega[n]==3, 1, 0], {n, 2500}], {1, 1}][[All, 1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 02 2017 *)
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PROG
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(Haskell)
twinLow [] = []
twinLow [_] = []
twinLow (n : (m : ns))
| m == n + 1 = n : twinLow (m : ns)
| otherwise = twinLow (m : ns)
a215217 n = (twinLow a007304_list) !! (n - 1)
(PARI) is_a033992(n) = omega(n)==3 && bigomega(n)==3
is(n) = is_a033992(n) && is_a033992(n+1) \\ Felix Fröhlich, Jun 10 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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