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URL: https://oeis.org/A369854

⇱ A369854 - OEIS

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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
OFFSET
0,4
LINKS
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 *)
KEYWORD
nonn
AUTHOR
Clark Kimberling, Feb 03 2024
EXTENSIONS
a(23)-a(36) from Alois P. Heinz, Feb 03 2024
STATUS
approved