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A334768 Self-convolution of A061397. 1
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 (list; graph; refs; listen; history; text; internal format)
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 A238581 A063608

Adjacent sequences:  A334765 A334766 A334767 * A334769 A334770 A334771

KEYWORD

nonn,easy

AUTHOR

Lawrence Pepper, May 10 2020

STATUS

approved

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Last modified September 29 21:59 EDT 2020. Contains 337432 sequences. (Running on oeis4.)