A193315 Write 2n=j+q (j,q positive noncomposite numbers); j*q maximal; then a(n)=j*q.

1, 4, 9, 15, 25, 35, 49, 55, 77, 91, 121, 143, 169, 187, 221, 247, 289, 323, 361, 391, 437, 403, 529, 551, 589, 667, 713, 703, 841, 899, 961, 943, 1073, 1147, 1189, 1271, 1369, 1363, 1517, 1591, 1681, 1763, 1849, 1927, 2021, 1891, 2209, 2279, 2257, 2491, 2537, 2623, 2809, 2867, 2881

Offset: 1

Author

Juri-Stepan Gerasimov, Aug 26 2011

Keywords

• nonn

Comments

a(n) = A102084(n) for n > 0. [Reinhard Zumkeller, Aug 28 2011]

Examples

			At n=6, 2n=12; 12 = 1 + 11 = 7 + 5; 7*5 = maximal => j*q = 7*5 = 35.
		

Crossrefs

Cf. A073046, A008578, A061397.

Programs

Haskell

a193315 1 = 1
a193315 n = maximum $ zipWith (*) prims $ map (a061397 . (2*n -)) prims
   where prims = takeWhile (<= n) a008578_list
-- Reinhard Zumkeller, Aug 28 2011

Maple

isA008578 := proc(n) if n = 1 then true ; elif isprime(n) then true; else false; end if; end proc:
A193315 := proc(n) local mx,j,q ; mx := 0 ; for j from 1 to 2*n-1 do if isA008578(j) then q := 2*n-j ; if isA008578(q) then mx := max(mx,j*q) ; end if ; end if; end do: mx ; end proc:
seq(A193315(n),n=1..60) ; # R. J. Mathar, Aug 28 2011

Sage

def is_A008578(n): return n == 1 or is_prime(n)
def A193315(n): return max((j*(2*n-j)) for j in [1]+prime_range(n+1) if is_A008578(2*n-j))
[A193315(i) for i in range(1,15)]
# D. S. McNeil, Aug 27 2011