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A334768 Self-convolution of A061397.

%I A334768 #31 May 12 2020 04:15:53
%S A334768 0,0,0,0,4,12,9,20,30,28,67,0,70,44,115,52,188,0,284,68,284,76,405,0,
%T A334768 714,92,573,0,604,0,1182,116,668,124,1271,0,1960,0,795,148,1642,0,
%U A334768 2680,164,1570,172,2183,0,3974,188,3024,0,2706,0,5354,212,2842,0,3799
%N A334768 Self-convolution of A061397.
%C A334768 If any term of even index greater than 2 is equal to 0 then the Goldbach conjecture would be disproved.
%H A334768 Alois P. Heinz, <a href="/A334768/b334768.txt">Table of n, a(n) for n = 0..10000</a>
%F A334768 a(n) = Sum_{k=1..n-1} P(k)*P(n-k) where P(k) = A061397(k).
%p A334768 a:= n-> (f-> add(f(j)*f(n-j), j=0..n))(k-> `if`(isprime(k), k, 0)):
%p A334768 seq(a(n), n=0..60);  # _Alois P. Heinz_, May 11 2020
%t A334768 Table[Sum[If[PrimeQ[k], k, 0]*If[PrimeQ[n-k], n-k, 0], {k, 0, n}], {n, 0, 100}] (* _Vaclav Kotesovec_, May 10 2020 *)
%o A334768 (Python)
%o A334768 def a(n):
%o A334768     A061397 = [0]+[factorial(2*i-1)%(i**2) for i in range(1,n+1)]
%o A334768     sum = 0
%o A334768     for i in range(1,n):
%o A334768         sum += A061397[i] * A061397[n-i]
%o A334768     return sum
%o A334768 (PARI) P(n) = if (isprime(n), n);
%o A334768 a(n) = sum(k=1, n-1, P(k)*P(n-k)); \\ _Michel Marcus_, May 10 2020
%Y A334768 Cf. A000040, A010051, A061397, A073610.
%K A334768 nonn,easy
%O A334768 0,5
%A A334768 _Lawrence Pepper_, May 10 2020