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A243485 Sum of all the products formed by multiplying the corresponding smaller and larger parts of the Goldbach partitions of n. 3
0, 0, 0, 4, 6, 9, 10, 15, 14, 46, 0, 35, 22, 82, 26, 94, 0, 142, 34, 142, 38, 263, 0, 357, 46, 371, 0, 302, 0, 591, 58, 334, 62, 780, 0, 980, 0, 578, 74, 821, 0, 1340, 82, 785, 86, 1356, 0, 1987, 94, 1512, 0, 1353, 0, 2677, 106, 1421, 0, 2320, 0, 4242, 118 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

a(n) is even for odd n.

If Goldbach's conjecture is true, a(n) > 0 for all even n > 2.

Sum of the areas of the distinct rectangles with prime length and width such that L + W = n, W <= L. For example, a(16) = 94; the two rectangles are 3 X 13 and 5 X 11, and the sum of their areas is 3*13 + 5*11 = 94. - Wesley Ivan Hurt, Oct 28 2017

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Goldbach Partition

Wikipedia, Goldbach's conjecture

Index entries for sequences related to Goldbach conjecture

Index entries for sequences related to partitions

FORMULA

a(n) = Sum_{i=2..n/2} i*(n-i) * A064911(i*(n-i)).

a(n) = Sum_{i=1..floor(n/2)} i * (n-i) * A010051(i) * A010051(n-i). - Wesley Ivan Hurt, Oct 29 2017

MAPLE

with(numtheory): A243485:=n->add(i*(n-i)*(pi(i)-pi(i-1))*(pi(n-i)-pi(n-i-1)), i=1..floor(n/2)): seq(A243485(n), n=1..100); # Wesley Ivan Hurt, Oct 29 2017

MATHEMATICA

Table[Sum[i*(n - i)*Floor[2/PrimeOmega[i (n - i)]], {i, 2, n/2}], {n,

  50}]

CROSSREFS

Cf. A002372, A002375, A045917, A064911, A117929.

Sequence in context: A189553 A189482 A099303 * A005659 A010462 A028957

Adjacent sequences:  A243482 A243483 A243484 * A243486 A243487 A243488

KEYWORD

nonn,easy,changed

AUTHOR

Wesley Ivan Hurt, Jun 05 2014

STATUS

approved

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Last modified February 18 04:10 EST 2018. Contains 299298 sequences. (Running on oeis4.)