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

0,4

Comments

Sum of all the primes appearing in columns less than or equal to n from the example in A258087.

Links

Table of n, a(n) for n=0..62.

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 *)

Crossrefs

Cf. A010051, A258087.

Partial Sums of A288726.

Sequence in context: A213041 A293330 A135541 * A180804 A122264 A079824

Adjacent sequences: A288653 A288654 A288655 * A288657 A288658 A288659

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Jun 12 2017

Status

approved