id:A056172 - OEIS Search Results

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Number of non-unitary prime divisors of n!.

+0
7

0, 0, 0, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14 (list; graph; listen)

	OFFSET	`1,6`
	COMMENT	`A non-unitary prime divisor for n! is not larger than n/2. a(n)=PrimePi[n/2]`
	FORMULA	`A prime divisor of x is not unitary iff its exponent is at least 2 in prime power factorization of x. In general GCD[p, x/p]=1 or p. Cases are counted when GCD[p, n/p]>1.`
	EXAMPLE	`10!=2.2.2.2.2.2.2.2.3.3.3.3.5.5.7 The non-unitary prime divisors is 2,3,5 because their exponents exceed 1, so a(10)=3, while 10! has only 5 unitary prime divisor.`
	CROSSREFS	`A001221, A034444, A000720, A048105, A048656, A048657.` `Sequence in context: A108956 A108037 A055679 this_sequence A091373 A008621 A002265` `Adjacent sequences: A056169 A056170 A056171 this_sequence A056173 A056174 A056175`
	KEYWORD	`nonn`
	AUTHOR	`Labos E. (labos(AT)ana.sote.hu), Jul 27 2000`

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Last modified July 25 07:41 EDT 2008. Contains 142293 sequences.

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