login
A279726
Partial sums of A187619.
1
0, 0, 0, 2, 6, 8, 16, 32, 44, 64, 92, 118, 150, 174, 202, 234, 298, 358, 382, 440, 512, 598, 686, 808, 924, 1002, 1130, 1228, 1336, 1480, 1560, 1762, 1966, 2026, 2210, 2426, 2614, 2840, 3132, 3300, 3496, 3812, 4072, 4240, 4616, 4852, 5068, 5402, 5522, 5826, 6234, 6512
OFFSET
1,4
FORMULA
a(n) = 2 * Sum_{k=1..n} (Sum_{i=3..k} A010051(i) * A010051(2k-i) * (k-i)).
MAPLE
with(numtheory): a:=n->2*add(add( (pi(i)-pi(i-1)) * (pi(2*k-i)-pi(2*k-i-1)) * (k-i), i=3..k), k=1..n): seq(a(n), n=1..100);
MATHEMATICA
Accumulate@ Table[2 Sum[Boole[PrimeQ@ i] Boole[PrimeQ[2 n - i]] (n - i), {i, 3, n}], {n, 56}] (* Michael De Vlieger, Dec 17 2016 *)
CROSSREFS
Sequence in context: A191822 A238549 A237502 * A337881 A331974 A137848
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Dec 17 2016
STATUS
approved