A080774 Numbers with two prime factors: (4*i+1)*(4*j+3).

15, 35, 39, 51, 55, 87, 91, 95, 111, 115, 119, 123, 143, 155, 159, 183, 187, 203, 215, 219, 235, 247, 259, 267, 287, 291, 295, 299, 303, 319, 323, 327, 335, 339, 355, 371, 391, 395, 403, 407, 411, 415, 427, 447, 451, 471, 511, 515, 519, 527, 535, 543, 551

Offset: 1

Author

Reinhard Zumkeller, Mar 10 2003

Keywords

• nonn

Comments

Semiprimes of the form 4k+3. - Giovanni Teofilatto, Jun 15 2005

There are 971 semiprimes of the form 4k+3 below 10,000.

Examples

			a(1) = 15 = 3*5 = (4*1+1)*(4*0+3).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)
• Eric Weisstein's World of Mathematics, Semiprime.
• Wikipedia, Semiprime.

Crossrefs

Cf. A001358, A006881, A002144, A002145, A107978, A121387.

Programs

Mathematica

Select[Range[15, 1000, 2], Last /@ FactorInteger[#] == {1, 1} && IntegerQ[(# - 3)/4] &] (* Vladimir Joseph Stephan Orlovsky, May 07 2011 *)
Select[4*Range[200]+3,PrimeOmega[#]==2&] (* Harvey P. Dale, Nov 02 2024 *)

PARI

isok(k) = k % 4 == 3 && bigomega(k) == 2; \\ Amiram Eldar, Jun 15 2025