A089820 - OEIS

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A089820

Number of subsets of {1,.., n} containing at least one prime.

0, 2, 6, 12, 28, 56, 120, 240, 480, 960, 1984, 3968, 8064, 16128, 32256, 64512, 130048, 260096, 522240, 1044480, 2088960, 4177920, 8372224, 16744448, 33488896, 66977792, 133955584, 267911168, 536346624, 1072693248 (list; graph; refs; listen; history; internal format)

	OFFSET	`1,2`
	COMMENTS	`a(n) = Sum(A089818(n,k): 1<=k<=A000720(n)) = A000079(n)-A089819(n) = A089819(n)*A000225(A000720(n)).`
	FORMULA	`a(n) = 2^n - 2^(n-pi(n)) = the total number of subsets minus the number of subsets of the nonprime elements of {1, ..., n}, where pi = A000720. - Greg Martin (gerg(AT)math.ubc.ca), May 13 2004`
	CROSSREFS	`Cf. A089822.` `Sequence in context: A159553 A112510 A011949 * A122746 A191394 A183467` `Adjacent sequences: A089817 A089818 A089819 * A089821 A089822 A089823`
	KEYWORD	`nonn`
	AUTHOR	`Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 12 2003`

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Last modified February 15 07:58 EST 2012. Contains 205717 sequences.