A089820 - OEIS

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

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OFFSET

1,2

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

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

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 *)

PROG

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

CROSSREFS

Cf. A089822.

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

Sequence in context: A284449 A011949 A350271 * A122746 A191394 A237500

Adjacent sequences: A089817 A089818 A089819 * A089821 A089822 A089823

KEYWORD

nonn,easy

AUTHOR

Reinhard Zumkeller, Nov 12 2003

EXTENSIONS

More terms from Wesley Ivan Hurt, Sep 19 2014

STATUS

approved