A248202 Sphenic numbers (A007304) whose neighbors are sphenic.

1310, 1886, 2014, 2666, 3730, 5134, 6062, 6214, 6306, 6478, 6854, 6986, 7258, 7954, 8394, 8534, 8786, 9214, 9454, 9822, 9878, 10282, 10946, 11606, 12454, 12566, 12802, 12858, 12994, 13054, 14134, 14314, 14330, 14466, 14818, 15086, 15266, 15806, 16114, 16134

Offset: 1

Author

James G. Merickel, Oct 03 2014

Keywords

• nonn

Comments

Subsequence of A169834 and offset by 1 from the values in A066509.

Examples

			1309, 1310 and 1311 factor as 7*11*17, 2*5*131 and 3*19*23, respectively.  No smaller such trio exists, so a(1)=1310.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000
• Wikipedia, Sphenic number

Crossrefs

Cf. A007304, A169834, A066509, A248201, A248203, A248204, A259349, A259350, A259801.

Programs

Mathematica

a248202[n_Integer] := Select[Range[n],
  And[And[PrimeNu[#] == 3, PrimeNu[# - 1] == 3, PrimeNu[# + 1] == 3], And[PrimeOmega[#] == 3, PrimeOmega[# - 1] == 3, PrimeOmega[# + 1] == 3]] &]; a248202[20166](* Michael De Vlieger, Nov 06 2014 *)
f[n_]:=Last/@FactorInteger[n]=={1, 1, 1}; lst={}; Do[If[f[n]&&f[n+1]&&f[n+2], AppendTo[lst, n + 1]], {n, 17000}]; lst (* Vincenzo Librandi, Jul 24 2015 *)
Mean/@SequencePosition[Table[If[PrimeNu[n]==PrimeOmega[n]==3,1,0],{n,20000}],{1,1,1}] (* Harvey P. Dale, Dec 08 2024 *)

PARI

sq(n)=bigomega(n)==3 && omega(n)==3;
for(n=3,10^5,if(sq(n-1)&&sq(n)&&sq(n+1),print1(n,", ")));
\\ Joerg Arndt, Oct 18 2014

Formula

a(n) = A066509(n)+1.