id:A161942 - OEIS Search Results

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A161942

Odd part of sum of divisors of n.

+0
3

1, 3, 1, 7, 3, 3, 1, 15, 13, 9, 3, 7, 7, 3, 3, 31, 9, 39, 5, 21, 1, 9, 3, 15, 31, 21, 5, 7, 15, 9, 1, 63, 3, 27, 3, 91, 19, 15, 7, 45, 21, 3, 11, 21, 39, 9, 3, 31, 57, 93, 9, 49, 27, 15, 9, 15, 5, 45, 15, 21, 31, 3, 13, 127, 21, 9, 17, 63, 3, 9, 9, 195, 37, 57, 31, 35, 3, 21, 5, 93, 121, 63 (list; graph; listen)

	OFFSET	`1,2`
	COMMENT	`It is conjectured that iteration of this function will always reach 1. This implies the non-existence of odd perfect numbers. This is equivalent to the same question for A000593, which can be expressed as the sum of the divisors of the odd part of n.` `Up to 20000000, there are only two odd numbers with a(n) and a(a(n)) both >= n: 81 and 18966025.`
	FORMULA	`Multiplicative with a(p^e) = oddpart((p^{e+1}-1)/(p-1)), where oddpart(n) = A000265(n) is the largest odd divisor of n.`
	PROGRAM	`(PARI) oddpart(n)=n/2^valuation(n, 2)` `a(n)=oddpart(sigma(n))`
	CROSSREFS	`Cf. A000265, A000203, A000593` `Sequence in context: A130330 A050227 A135540 this_sequence A053092 A115873 A083239` `Adjacent sequences: A161939 A161940 A161941 this_sequence A161943 A161944 A161945`
	KEYWORD	`easy,mult,nonn`
	AUTHOR	`Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Jun 22 2009`

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Last modified December 9 14:43 EST 2009. Contains 170430 sequences.

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