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

1,1

Comments

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

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Wikipedia, Sphenic number

Formula

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

Example

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.

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A165936 A242606 A066509 * A256668 A205301 A320506

Adjacent sequences: A248199 A248200 A248201 * A248203 A248204 A248205

Keyword

nonn,changed

Author

James G. Merickel, Oct 03 2014

Status

approved