A288656 a(n) = Sum_{k=1..n} Sum_{i=floor((k-1)/2)..k-1} i * c(i), where c is the prime characteristic (A010051).
0, 0, 0, 2, 7, 12, 22, 30, 45, 57, 69, 81, 104, 122, 153, 184, 215, 239, 280, 321, 381, 441, 501, 561, 644, 716, 788, 860, 932, 991, 1079, 1167, 1286, 1405, 1524, 1643, 1762, 1864, 2003, 2142, 2281, 2401, 2562, 2723, 2927, 3131, 3335, 3539, 3790, 4018, 4246, 4474, 4702, 4930, 5211, 5492, 5773, 6054, 6335, 6616, 6956, 7267, 7639
Offset: 0
Programs
-
Maple
with(numtheory): A288656:=n->add(add(i*(pi(i)-pi(i-1)), i=floor((k-1)/2)..k-1), k=1..n): seq(A288656(n), n=0..100);
-
Mathematica
Table[Sum[Sum[i (PrimePi[i] - PrimePi[i - 1]), {i, Floor[(k - 1)/2], k - 1}], {k, n}], {n, 0, 62}] (* Michael De Vlieger, Jun 15 2017 *)
Comments