cp's OEIS Frontend

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.

%I A279536 #22 Feb 16 2025 08:33:38
%S A279536 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,
%T A279536 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,
%U A279536 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
%N 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.
%C A279536 a(n) >= A279315(n). - _Wesley Ivan Hurt_, Dec 17 2016
%H A279536 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GoldbachPartition.html">Goldbach Partition</a>
%H A279536 Wikipedia, <a href="http://en.wikipedia.org/wiki/Goldbach%27s_conjecture">Goldbach's conjecture</a>
%H A279536 <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>
%H A279536 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A279536 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))))), where mu is the Möbius function (A008683).
%p A279536 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);
%Y A279536 Cf. A008683, A010051, A279315.
%K A279536 nonn,easy
%O A279536 1,4
%A A279536 _Wesley Ivan Hurt_, Dec 14 2016