OFFSET
1,1
COMMENTS
Every semiprime not divisible by 2 or 3 must be in one of these three disjoint sets:
A108172 - the product of a prime of the form 6n + 1 and a prime of the form 6n - 1.
The product of two primes of the form 6n - 1 is a semiprime of the form 6n + 1.
REFERENCES
Milton Abramowitz and Irene A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 870.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Milton Abramowitz and Irene A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
FORMULA
{a(n)} = {p*q where both p and q are in A007528}.
MATHEMATICA
Module[{nn = 150, pf}, pf = Select[6Range[nn] - 1, PrimeQ]; Take[Union[Times@@@Tuples[pf, 2]], nn/2]] (* Harvey P. Dale, Dec 09 2013 *)
Select[6Range[200] + 1, PrimeOmega[#] == 2 && Mod[FactorInteger[#][[1, 1]], 6] == 5 &] (* Alonso del Arte, Aug 24 2017 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Jun 13 2005
EXTENSIONS
Edited and extended by Ray Chandler, Oct 15 2005
STATUS
approved