id:A091304 - OEIS Search Results

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Omega(2n+1) (prime factors counted with multiplicity).

+0
4

1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 3, 1, 1, 2, 2, 1, 2, 1, 1, 3, 1, 2, 2, 1, 2, 2, 1, 1, 3, 2, 1, 2, 1, 1, 3, 2, 1, 4, 1, 2, 2, 1, 2, 2, 2, 1, 3, 1, 1, 3, 1, 1, 2, 1, 2, 3, 2, 2, 2, 3, 1, 2, 1, 2, 4, 1, 1, 2, 2, 2, 3, 1, 1, 3, 2, 1, 2, 2, 1, 3, 1, 2, 3, 1, 3, 2, 1, 1, 1, 2, 2, 4, 1, 1, 3, 1, 1, 2, 2, 2, 3, 2 (list; graph; listen)

	OFFSET	`0,5`
	COMMENT	`Omega(n) of the odd integers follows a pattern similar to A001222, with 4 maxima instead of 2 - i.e. between 2^n and (2^(n+1) - 1) there are two numbers with exactly n factors (2^n and 2^(n-1) * 3) while the odd integers have 4 maxima (3^n, 3^(n-1) * 5, 3^(n-1) * 7, 5^2*3^(n-2)) between 3^n and 3^(n+1) - 1.`
	FORMULA	`Odd members of A001222, generated using the function Omega(n)`
	EXAMPLE	`Omega(1) = 1, Omega(9) = 2 (3 * 3 = 9), Omega (243) = 5 (3 * 3 * 3 * 3 * 3 = 243), Omega(51) = 2 (3 * 17 = 51)`
	CROSSREFS	`Cf. A001222.` `Sequence in context: A103956 A103957 A091853 this_sequence A049847 A025431 A161070` `Adjacent sequences: A091301 A091302 A091303 this_sequence A091305 A091306 A091307`
	KEYWORD	`easy,nonn`
	AUTHOR	`Andrew Plewe (aplewe(AT)sbcglobal.net), Feb 20 2004`

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Last modified December 10 12:37 EST 2009. Contains 170569 sequences.

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