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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.)