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A193315 Write 2n=j+q (j,q positive noncomposite numbers); j*q maximal; then a(n)=j*q. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..55.

EXAMPLE

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

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

PROG

(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

(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

CROSSREFS

Cf. A073046, A008578, A061397.

Sequence in context: A050530 A278021 A102084 * A030664 A070160 A244672

Adjacent sequences:  A193312 A193313 A193314 * A193316 A193317 A193318

KEYWORD

nonn

AUTHOR

Juri-Stepan Gerasimov, Aug 26 2011

STATUS

approved

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Last modified May 27 21:52 EDT 2020. Contains 334671 sequences. (Running on oeis4.)