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 A369854 a(n) = number of nonempty subsets S of {1,2,...,n} such that (number of nonprimes in S) = (number of primes in S). 4
 0, 0, 1, 2, 5, 9, 19, 34, 69, 125, 209, 461, 791, 1715, 3002, 5004, 8007, 19447, 31823, 75581, 125969, 203489, 319769, 817189, 1307503, 2042974, 3124549, 4686824, 6906899, 20030009, 30045014, 84672314, 129024479, 193536719, 286097759, 417225899, 600805295 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..2000 FORMULA a(n) = A369781(n) - A369853(n). a(n) = A037031(n) - 1 = binomial(n,pi(n)) - 1. - Alois P. Heinz, Feb 03 2024 EXAMPLE a(5) = 9 counts these subsets: {1,2}, {1,3}, {1,5}, {2,4}, {3,4}, {4,5}, {1,2,3,4}, {1,2,4,5}, {1,3,4,5}. MAPLE a:= n-> binomial(n, numtheory[pi](n))-1: seq(a(n), n=0..36); # Alois P. Heinz, Feb 03 2024 MATHEMATICA Map[Length[Select[Map[Commonest, PrimeQ[Rest[Subsets[Range[#]]]]], # == {False, True} || # == {True, False} &]] &, Range[22]] (* Peter J. C. Moses, Jan 29 2024 *) CROSSREFS Cf. A000040, A000720, A018252, A037031, A369780, A369781, A369853. Sequence in context: A073118 A048082 A089089 * A014495 A056326 A280247 Adjacent sequences: A369851 A369852 A369853 * A369855 A369856 A369857 KEYWORD nonn AUTHOR Clark Kimberling, Feb 03 2024 EXTENSIONS a(23)-a(36) from Alois P. Heinz, Feb 03 2024 STATUS approved

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Last modified May 19 09:42 EDT 2024. Contains 372683 sequences. (Running on oeis4.)