A215217 Smaller member of a pair of sphenic twins, consecutive integers, each the product of three distinct primes.

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

Offset: 1

Author

Martin Renner, Aug 06 2012

Keywords

• nonn

Comments

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.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A007304, A066509, A140077.

Programs

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)
-- Peter Dolland, May 31 2019

Maple

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

Mathematica

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 *)

PARI

is_a033992(n) = omega(n)==3 && bigomega(n)==3
is(n) = is_a033992(n) && is_a033992(n+1) \\ Felix Fröhlich, Jun 10 2019