A089820 Number of subsets of {1,..,n} containing at least one prime.

0, 2, 6, 12, 28, 56, 120, 240, 480, 960, 1984, 3968, 8064, 16128, 32256, 64512, 130048, 260096, 522240, 1044480, 2088960, 4177920, 8372224, 16744448, 33488896, 66977792, 133955584, 267911168, 536346624, 1072693248, 2146435072, 4292870144, 8585740288

Offset: 1

Author

Reinhard Zumkeller, Nov 12 2003

Keywords

• nonn
• easy

Comments

a(n) = Sum(A089818(n,k): 1<=k<=A000720(n)) = A000079(n)-A089819(n) = A089819(n)*A000225(A000720(n)).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A089822.

Cf. A000079, A000225, A000720, A089818, A089819.

Programs

Magma

[2^n-2^(n-#PrimesUpTo(n)) : n in [1..30]]; // Wesley Ivan Hurt, Sep 19 2014

Maple

with(numtheory): A089820:=n->2^n - 2^(n-pi(n)): seq(A089820(n), n=1..30); # Wesley Ivan Hurt, Sep 19 2014

Mathematica

Table[2^n - 2^(n - PrimePi[n]), {n, 30}] (* Wesley Ivan Hurt, Sep 19 2014 *)

Formula

a(n) = 2^n - 2^(n-pi(n)) = the total number of subsets minus the number of subsets of the nonprime elements of {1,..,n}, where pi = A000720. - Greg Martin, May 13 2004

Extensions

More terms from Wesley Ivan Hurt, Sep 19 2014