A073046 Write 2*n = p+q (p,q prime), p*q minimal; then a(n) = p*q.

4, 9, 15, 21, 35, 33, 39, 65, 51, 57, 95, 69, 115, 161, 87, 93, 155, 217, 111, 185, 123, 129, 215, 141, 235, 329, 159, 265, 371, 177, 183, 305, 427, 201, 335, 213, 219, 365, 511, 237, 395, 249, 415, 581, 267, 445, 623, 1501, 291, 485, 303, 309, 515, 321, 327

Offset: 2

Author

Werner D. Sand, Aug 31 2002

Keywords

• nonn

Comments

Least semiprime whose sum of prime factors equals 2*n.

Assuming Goldbach's conjecture, a(n) exists for all n >= 2. - David James Sycamore, Jan 08 2019

Examples

			n=13: 2n=26; 26 = 23 + 3 = 19 + 7 = 13 + 13; 23*3 = minimal => p*q = 23*3 = 69.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A000040, A061397.

Cf. A102084, A193315, A288814.

Programs

Haskell

a073046 n = head $ dropWhile (== 0) $
                   zipWith (*) prims $ map (a061397 . (2*n -)) prims
   where prims = takeWhile (<= n) a000040_list
-- Reinhard Zumkeller, Aug 28 2011

Mathematica

Array[Block[{p = 2, q}, While[! PrimeQ@ Set[q, 2 # - p], p = NextPrime[p]]; p q] &, 55, 2] (* Michael De Vlieger, Aug 02 2020 *)

Formula

For all n except 3, a(n) = A288814(2*n). - David James Sycamore, Jan 08 2019

Extensions

Corrected by Ray Chandler, Jun 11 2005