A369854 a(n) = number of nonempty subsets S of {1,2,...,n} such that (number of nonprimes in S) = (number of primes in S).

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

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