A107978 Products of two primes of the form 4n+3 (A002145).

9, 21, 33, 49, 57, 69, 77, 93, 121, 129, 133, 141, 161, 177, 201, 209, 213, 217, 237, 249, 253, 301, 309, 321, 329, 341, 361, 381, 393, 413, 417, 437, 453, 469, 473, 489, 497, 501, 517, 529, 537, 553, 573, 581, 589, 597, 633, 649, 669, 681, 713, 717, 721, 737

Offset: 1

Author

Jonathan Vos Post, Jun 12 2005

Keywords

• easy
• nonn

Comments

Every odd semiprime must be in one of three disjoint sets: the product of two primes of the form 4n+1 (A121387), the product of two primes of the form 4n+3 (A107978), or the product of a prime of the form 4n+1 and a prime of the form 4n+3 (A080774).

Links

• T. D. Noe, Table of n, a(n) for n=1..1000
• Eric Weisstein's World of Mathematics, Semiprime.

Crossrefs

Cf. A001358, A002145, A080774, A121387.

Union of A131574 and A080109.

Third row of A121388.

Programs

Mathematica

p = Select[ Prime@ Range@ 60, Mod[ #, 4] == 3 &]; Take[ Sort@ Flatten@ Table[ p[[i]] p[[j]], {j, 30}, {i, j}], 54] (* or *)
fQ[n_] := Block[{fi = FactorInteger@ n}, Plus @@ Last /@ fi == 2 && Union@ Mod[ First /@ fi, 4] == {3}]; Select[ Range@ 748, fQ@# &] (* Robert G. Wilson v, May 20 2010 *)

Formula

{a(n)} = {p*q: p and q both elements of A002145}.

Extensions

Edited by N. J. A. Sloane, May 20 2010