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 A256885 a(n) = n*(n + 1)/2 - pi(n), where pi(n) = A000720(n) is the prime counting function. 2
 1, 2, 4, 8, 12, 18, 24, 32, 41, 51, 61, 73, 85, 99, 114, 130, 146, 164, 182, 202, 223, 245, 267, 291, 316, 342, 369, 397, 425, 455, 485, 517, 550, 584, 619, 655, 691, 729, 768, 808, 848, 890, 932, 976, 1021, 1067, 1113, 1161, 1210, 1260, 1311, 1363, 1415, 1469, 1524 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Number of lattice points (x,y) in the region 1 <= x <= n, 1 <= y <= n - A010051(n); see example. This sequence gives the row sums of the triangle A257232. - Wolfdieter Lang, Apr 21 2015 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 Eric Weisstein's World of Mathematics, Prime Counting Function Wikipedia, Prime-counting function FORMULA a(n) = A000217(n) - A000720(n). a(n) - a(n-1) = A014684(n), n >= 2. a(n) = Sum_{i=1..n} A014684(i). a(n) = 1 + Sum_{i=2..n}(i - A000720(i) + A000720(i-1)). EXAMPLE 10 .                             x 9  .                          x  x 8  .                       x  x  x 7  .                    .  x  x  x 6  .                 x  x  x  x  x 5  .              .  x  x  x  x  x 4  .           x  x  x  x  x  x  x 3  .        .  x  x  x  x  x  x  x 2  .     .  x  x  x  x  x  x  x  x 1  .  x  x  x  x  x  x  x  x  x  x 0  .__.__.__.__.__.__.__.__.__.__.    0  1  2  3  4  5  6  7  8  9  10 MAPLE with(numtheory)[pi]: A256885:=n->n*(n+1)/2-pi(n): seq(A256885(n), n=1..100); MATHEMATICA Table[n (n + 1)/2 - PrimePi[n], {n, 1, 50}] PROG (MAGMA) [n*(n + 1)/2 - #PrimesUpTo(n): n in [1..60] ]; // Vincenzo Librandi, Apr 12 2015 (PARI) vector(80, n, n*(n+1)/2 - primepi(n)) \\ Michel Marcus, Apr 13 2015 (Haskell) a256885 n = a000217 n - a000720 n  -- Reinhard Zumkeller, Apr 21 2015 CROSSREFS Cf. A000217, A000720, A010051, A014684, A113638, A257232. Sequence in context: A100057 A007590 A080476 * A293495 A053799 A284122 Adjacent sequences:  A256882 A256883 A256884 * A256886 A256887 A256888 KEYWORD nonn,easy AUTHOR Wesley Ivan Hurt, Apr 11 2015 EXTENSIONS Edited, following the hint by Reinhard Zumkeller to change the offset. - Wolfdieter Lang, Apr 22 2015 STATUS approved

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Last modified July 18 21:25 EDT 2019. Contains 325144 sequences. (Running on oeis4.)