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A089822 Number of subsets of {1,.., n} containing exactly two primes. 5
0, 0, 2, 4, 12, 24, 48, 96, 192, 384, 640, 1280, 1920, 3840, 7680, 15360, 21504, 43008, 57344, 114688, 229376, 458752, 589824, 1179648, 2359296, 4718592, 9437184, 18874368, 23592960, 47185920, 57671680, 115343360, 230686720 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

a(n) = A000217(A000720(n)-1)*A089819(n);

for n>2: a(n) = A089818(n,2).

LINKS

Robert Israel, Table of n, a(n) for n = 1..3830

FORMULA

a(n) = (pi(n)*(pi(n)-1)*2^(n-pi(n)))/2, with pi = A000720.

EXAMPLE

a(5)=12 subsets of {1,2,3,4,5} contain exactly two primes: {2,3},

{2,5}, {3,5}, {1,2,3}, {1,2,5}, {1,3,5}, {2,3,4}, {2,4,5}, {3,4,5},

{1,2,3,4}, {1,2,4,5} and {1,3,4,5}.

MAPLE

N:= 100: # for a(1)..a(N)

V:= Vector(N):

p:= 1: n:= 1: pi:= 0:

while n <= N do

  p:= nextprime(p);

  for n from n to min(N, p-1) do

    V[n]:= pi*(pi-1)*2^(n-pi)/2;

  od;

  pi:= pi+1;

  n:= p;

od:

convert(V, list); # Robert Israel, Jul 14 2019

CROSSREFS

Cf. A089819, A089821.

Sequence in context: A230481 A212169 A108720 * A079352 A089888 A291779

Adjacent sequences:  A089819 A089820 A089821 * A089823 A089824 A089825

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Nov 12 2003

STATUS

approved

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Last modified October 13 21:59 EDT 2019. Contains 327981 sequences. (Running on oeis4.)