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A309160 Number of nonempty subsets of [n] whose elements have a prime average. 1
0, 1, 4, 6, 11, 15, 22, 40, 72, 118, 199, 355, 604, 920, 1306, 1906, 3281, 6985, 16446, 38034, 82490, 168076, 325935, 604213, 1068941, 1815745, 3038319, 5246725, 9796132, 19966752, 42918987, 92984247, 197027405, 402932711, 792381923, 1499918753, 2746078246 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..200

FORMULA

a(n) < A051293(n).

EXAMPLE

a(3) = 4 because 4 of the subsets of [3], namely {2}, {3}, {1,3}, {1,2,3}, have prime averages.

MAPLE

b:= proc(n, s, c) option remember; `if`(n=0,

      `if`(c>0 and denom(s)=1 and isprime(s), 1, 0),

       b(n-1, s, c)+b(n-1, (s*c+n)/(c+1), c+1))

    end:

a:= n-> b(n, 0$2):

seq(a(n), n=1..40);  # Alois P. Heinz, Jul 15 2019

MATHEMATICA

a[n_]:=Length[Select[Subsets[Range[n]], PrimeQ[Mean[#]]&]]; a/@Range[25]

CROSSREFS

Cf. A051293, A114976, A127542.

Sequence in context: A036831 A084263 A232807 * A266795 A060180 A190499

Adjacent sequences:  A309157 A309158 A309159 * A309161 A309162 A309163

KEYWORD

nonn

AUTHOR

Ivan N. Ianakiev, Jul 15 2019

EXTENSIONS

a(26)-a(37) from Alois P. Heinz, Jul 15 2019

STATUS

approved

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Last modified January 29 10:34 EST 2020. Contains 331337 sequences. (Running on oeis4.)