login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A279536 Count the squarefree numbers appearing in each interval [p,q] where (p,q) is a Goldbach partition of 2n such that all primes from p to q (inclusive) appear as a part in some Goldbach partition of p+q = 2n, and then add the results. 3
0, 0, 1, 2, 5, 3, 1, 0, 9, 0, 1, 19, 1, 0, 21, 0, 1, 10, 1, 0, 4, 0, 1, 0, 0, 3, 0, 0, 1, 68, 1, 0, 0, 5, 0, 0, 1, 0, 4, 0, 1, 25, 1, 0, 3, 0, 1, 0, 0, 3, 0, 0, 8, 0, 0, 5, 0, 0, 1, 12, 1, 0, 0, 5, 0, 0, 1, 0, 4, 0, 1, 2, 1, 0, 0, 5, 0, 0, 1, 0, 14, 0, 1, 0, 0, 5, 0, 0, 1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

a(n) >= A279315(n). - Wesley Ivan Hurt, Dec 17 2016

LINKS

Table of n, a(n) for n=1..90.

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=3..n} (A010051(i) * A010051(2n-i) * (Sum_{j=i..2n-i} mu(j)^2) * (Product_{k=i..n} (1-abs(A010051(k)-A010051(2n-k))))).

MAPLE

with(numtheory): A279536:=n->add( (pi(i)-pi(i-1)) * (pi(2*n-i)-pi(2*n-i-1)) * add(mobius(j)^2, j=i..2*n-i) * (product(1-abs((pi(k)-pi(k-1))-(pi(2*n-k)-pi(2*n-k-1))), k=i..n)), i=3..n): seq(A279536(n), n=1..100);

CROSSREFS

Cf. A010051, A279315.

Sequence in context: A102892 A132898 A265318 * A269954 A234255 A062706

Adjacent sequences:  A279533 A279534 A279535 * A279537 A279538 A279539

KEYWORD

nonn,easy

AUTHOR

Wesley Ivan Hurt, Dec 14 2016

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 24 09:37 EDT 2019. Contains 323529 sequences. (Running on oeis4.)