|
|
A231967
|
|
Squarefree numbers (A005117) of the form p*q*r with prime factors p, q, r with q = 2*p + 1 and r = 2*q + 1.
|
|
4
|
|
|
110, 1265, 11891, 568301, 5719229, 46203659, 371436119, 1057570169, 2978731439, 8475105539, 8777935031, 14865764009, 22397944469, 24460553171, 26008879181, 27621202391, 47549400491, 53960155829, 54994829321, 57639193331, 119010782819, 157361958899
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Squarefree numbers of the form p*q*r, where p < q < r = primes with q = 2*p + 1 and r = 2*q + 1; that is, r = 4*p + 3.
|
|
LINKS
|
|
|
EXAMPLE
|
5719229 = 89*179*359, 179 = 2*89 + 1, 359 = 2*179 + 1.
|
|
MATHEMATICA
|
sfQ[n_]:=Module[{q=2n+1, r}, r=2q+1; AllTrue[{q, r}, PrimeQ]&& SquareFreeQ[ n*q*r]]; 3#+10#^2+8#^3&/@Select[Prime[Range[400]], sfQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 26 2016 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|