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A089821 Number of subsets of {1,.., n} containing exactly one prime. 3
0, 2, 4, 8, 12, 24, 32, 64, 128, 256, 320, 640, 768, 1536, 3072, 6144, 7168, 14336, 16384, 32768, 65536, 131072, 147456, 294912, 589824, 1179648, 2359296, 4718592, 5242880, 10485760, 11534336, 23068672, 46137344, 92274688, 184549376, 369098752, 402653184 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..37.

FORMULA

a(n) = A000720(n)*A089819(n);

for n>1: a(n) = A089818(n,1).

a(n) = pi(n) * 2^(n-pi(n)), with pi = A000720.

EXAMPLE

a(5)=12 subsets of {1,2,3,4,5} contain exactly one prime: {2}, {3}, {5}, {1,2}, {1,3}, {1,5}, {2,4}, {3,4}, {4,5}, {1,2,4}, {1,3,4} and {1,4,5}.

MAPLE

b:= proc(n, c) option remember; `if`(n=0, `if`(c=0, 1, 0),

     `if`(c<0, 0, b(n-1, c)+b(n-1, c-`if`(isprime(n), 1, 0))))

    end:

a:= n-> b(n, 1):

seq(a(n), n=1..42);  # Alois P. Heinz, Dec 19 2019

MATHEMATICA

b[n_, c_] := b[n, c] = If[n == 0, If[c == 0, 1, 0], If[c < 0, 0, b[n - 1, c] + b[n - 1, c - If[PrimeQ[n], 1, 0]]]];

a[n_] := b[n, 1];

Array[a, 42] (* Jean-François Alcover, Nov 07 2020, after Alois P. Heinz *)

PROG

(PARI) a(n) = primepi(n) * 2^(n-primepi(n)); \\ Michel Marcus, Nov 07 2020

CROSSREFS

Cf. A000720, A089818, A089819, A089822.

Sequence in context: A175841 A293601 A171647 * A343419 A353796 A294067

Adjacent sequences:  A089818 A089819 A089820 * A089822 A089823 A089824

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Nov 12 2003

STATUS

approved

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Last modified May 28 16:37 EDT 2022. Contains 354119 sequences. (Running on oeis4.)