A000885 -id:A000885 - cp's OEIS frontend

A000879 Number of primes < prime(n)^2.

2, 4, 9, 15, 30, 39, 61, 72, 99, 146, 162, 219, 263, 283, 329, 409, 487, 519, 609, 675, 705, 811, 886, 1000, 1163, 1252, 1294, 1381, 1423, 1523, 1877, 1976, 2141, 2190, 2489, 2547, 2729, 2915, 3043, 3241, 3436, 3512, 3868, 3945, 4089, 4164, 4627, 5106

Offset: 1

gandalf(AT)hrn.office.ssi.net (James D. Ausfahl)

nonn

a(n) is the least index i such that A052180(i) = prime(n). - Labos Elemer, May 14 2003
Number of primes determined at the n-th step of the sieve of Eratosthenes. - Jean-Christophe Hervé, Oct 21 2013
There are only 3 squares in the current data: 4, 9, 7745089. - Michel Marcus, Apr 07 2018
There are no other squares up to a(780000). - Giovanni Resta, Apr 09 2018

Donovan Johnson, Table of n, a(n) for n = 1..10000

Cf. A050216 (first differences), A089609, A052180, A000720, A001248, A000885, A054270 (primes of rank a(n)).

PrimePi[Prime[Range[50]]^2] (* Harvey P. Dale, Jan 16 2013 *)

a(n) = primepi(prime(n)^2); \\ Michel Marcus, Oct 28 2013

a(n) = A000720(A001248(n)). - Michel Marcus, Apr 07 2018

Edited by Ralf Stephan, Aug 24 2004

A230698 Triangle read by rows: T(n,k) = T(n-1,k-1) + n*T(n-2,k); T(0,0) = T(1,0) = T(1,1) = 1, T(n,k) = 0 if k>n or if k<0.

Original entry on oeis.org

1, 1, 1, 2, 1, 1, 3, 5, 1, 1, 8, 7, 9, 1, 1, 15, 33, 12, 14, 1, 1, 48, 57, 87, 18, 20, 1, 1, 105, 279, 141, 185, 25, 27, 1, 1, 384, 561, 975, 285, 345, 33, 35, 1, 1, 945, 2895, 1830, 2640, 510, 588, 42, 44, 1, 1, 3840, 6555, 12645, 4680, 6090, 840, 938, 52, 54, 1, 1

Offset: 0

Philippe Deléham, Oct 28 2013

Triangle A180048 mixed with triangle A180049.

Let p(n,x) be the polynomial whose coefficients are given by row n; e.g., p(2,x) = 2 + x + x^2; then p(n,x) is the numerator of the rational function given by f(n,x) = x + (n - 1)/f(n-1,x), where f(x,0) = 1. (Sum of numbers in row n) = A000885(n) for n >= 1. (Column 1) = A006882 (n-th term = n!! for n >= 0) - Clark Kimberling, Oct 19 2014

			Triangle begins (0<=k<=n):
1
1, 1
2, 1, 1
3, 5, 1, 1
8, 7, 9, 1, 1
15, 33, 12, 14, 1, 1
48, 57, 87, 18, 20, 1, 1
105, 279, 141, 185, 25, 27, 1, 1
384, 561, 975, 285, 345, 33, 35, 1, 1
945, 2895, 1830, 2640, 510, 588, 42, 44, 1, 1
3840, 6555, 12645, 4680, 6090, 840, 938, 52, 54, 1, 1
10395, 35685, 26685, 41685, 10290, 12558, 1302, 1422, 63, 65, 1, 1

Clark Kimberling, Rows 0..100, flattened

Cf. A180048, A180049.

t[0, 0] = 1; t[1, 0] = 1; t[1, 1] = 1; t[n_, k_] := t[n, k] = If[k > n || k < 0, 0, t[n - 1, k - 1] + n*t[n - 2, k]]; Table[t[n, k], {n, 0, 10}, {k, 0, n}](* Clark Kimberling, Oct 19 2014 *)
(* Next, the polynomials *); z = 20; f[x_, n_] := x + n/f[x, n - 1]; f[x_, 0] = 1; t = Table[Factor[f[x, n]], {n, 0, z}]; u = Numerator[t]; TableForm[Rest[Table[CoefficientList[u[[n]], x], {n, 0, z}]]]  (* A249057 array *)
Flatten[CoefficientList[u, x]] (* A249057 sequence *)
(* Clark Kimberling, Oct 19 2014 *)

T(n,k) = T(n-1,k-1) + n*T(n-2,k); T(0,0) = T(1,0) = T(1,1) = 1, T(n,k) = 0 if k>n or if k<0.
T(n,0) = A006882(n).
T(n+1,1) = A007911(n+3).
Sum_{k=0..n} T(n,k) = A000085(n+1).

Corrected by Clark Kimberling, Oct 21 2014

cp's OEIS Frontend

A000879 Number of primes < prime(n)^2.

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