A334768 Self-convolution of A061397.

0, 0, 0, 0, 4, 12, 9, 20, 30, 28, 67, 0, 70, 44, 115, 52, 188, 0, 284, 68, 284, 76, 405, 0, 714, 92, 573, 0, 604, 0, 1182, 116, 668, 124, 1271, 0, 1960, 0, 795, 148, 1642, 0, 2680, 164, 1570, 172, 2183, 0, 3974, 188, 3024, 0, 2706, 0, 5354, 212, 2842, 0, 3799

Offset

0,5

Comments

If any term of even index greater than 2 is equal to 0 then the Goldbach conjecture would be disproved.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Formula

a(n) = Sum_{k=1..n-1} P(k)*P(n-k) where P(k) = A061397(k).

Maple

a:= n-> (f-> add(f(j)*f(n-j), j=0..n))(k-> `if`(isprime(k), k, 0)):
seq(a(n), n=0..60);  # Alois P. Heinz, May 11 2020

Mathematica

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 *)

Prog

(Python)
def a(n):
    A061397 = [0]+[factorial(2*i-1)%(i**2) for i in range(1, n+1)]
    sum = 0
    for i in range(1, n):
        sum += A061397[i] * A061397[n-i]
    return sum
(PARI) P(n) = if (isprime(n), n);
a(n) = sum(k=1, n-1, P(k)*P(n-k)); \\ Michel Marcus, May 10 2020

Crossrefs

Cf. A000040, A010051, A061397, A073610.

Sequence in context: A229179 A273172 A307853 * A247327 A348419 A238581

Adjacent sequences: A334765 A334766 A334767 * A334769 A334770 A334771

Keyword

nonn,easy

Author

Lawrence Pepper, May 10 2020

Status

approved