

A107978


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


7



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


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.


FORMULA

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


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 *)


CROSSREFS

Cf. A001358, A002145, A080774, A121387.
Union of A131574 and A080109.
Third row of A121388.
Sequence in context: A017629 A216240 A176258 * A226355 A253052 A043112
Adjacent sequences: A107975 A107976 A107977 * A107979 A107980 A107981


KEYWORD

easy,nonn


AUTHOR

Jonathan Vos Post, Jun 12 2005


EXTENSIONS

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


STATUS

approved



