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A162142
Numbers that are the cube of a product of two distinct primes (p^3*q^3).
13
216, 1000, 2744, 3375, 9261, 10648, 17576, 35937, 39304, 42875, 54872, 59319, 97336, 132651, 166375, 185193, 195112, 238328, 274625, 328509, 405224, 456533, 551368, 614125, 636056, 658503, 753571, 804357, 830584, 857375, 1191016, 1367631, 1520875, 1643032
OFFSET
1,1
COMMENTS
Subset of A046306, of A000578, and of A007774. - R. J. Mathar, Jun 27 2009
FORMULA
a(n) = (A006881(n))^3 = A000578(A006881(n)). - R. J. Mathar, Jun 27 2009
Sum_{n>=1} 1/a(n) = (P(3)^2 - P(6))/2 = (A085541^2 - A085966)/2 = 0.006735..., where P is the prime zeta function. - Amiram Eldar, Jul 06 2020
EXAMPLE
216=2^3*3^3. 1000=2^3*5^3. 2744=2^3*7^3.
MATHEMATICA
fQ[n_]:=Last/@FactorInteger[n]=={3, 3}; lst={}; Do[If[fQ[n], AppendTo[lst, n]], {n, 6*9!}]; lst
With[{nn=30}, Select[Union[(Times@@@Subsets[Prime[Range[nn]], {2}])^3], #<= (2Prime[ nn])^3&]](* Harvey P. Dale, May 27 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Definition rephrased by R. J. Mathar, Jun 27 2009
STATUS
approved