id:A089820 - OEIS Search Results

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

+0
3

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; listen)

	OFFSET	`1,2`
	COMMENT	`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 this_sequence A141447 A122746 A057582` `Adjacent sequences: A089817 A089818 A089819 this_sequence A089821 A089822 A089823`
	KEYWORD	`nonn`
	AUTHOR	`Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 12 2003`

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Last modified November 23 17:09 EST 2009. Contains 167438 sequences.

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