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A073046 Write 2*n = p+q (p,q prime), p*q minimal; then a(n) = p*q. 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,1
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
LINKS
FORMULA
For all n except 3, a(n) = A288814(2*n). - David James Sycamore, Jan 08 2019
EXAMPLE
n=13: 2n=26; 26 = 23 + 3 = 19 + 7 = 13 + 13; 23*3 = minimal => p*q = 23*3 = 69.
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 *)
PROG
(Haskell)
a073046 n = head $ dropWhile (== 0) $
zipWith (*) prims $ map (a061397 . (2*n -)) prims
where prims = takeWhile (<= n) a000040_list
-- Reinhard Zumkeller, Aug 28 2011
CROSSREFS
Sequence in context: A103395 A103393 A103392 * A066495 A313298 A313299
KEYWORD
nonn
AUTHOR
Werner D. Sand, Aug 31 2002
EXTENSIONS
Corrected by Ray Chandler, Jun 11 2005
STATUS
approved

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Last modified April 13 09:16 EDT 2024. Contains 371640 sequences. (Running on oeis4.)