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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.)