

A248202


Sphenic numbers (A007304) whose neighbors are sphenic.


8



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
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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 *)


PROG

(PARI) sq(n)=bigomega(n)==3 && omega(n)==3;
for(n=3, 10^5, if(sq(n1)&&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


AUTHOR

James G. Merickel, Oct 03 2014


STATUS

approved



