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A161942
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Odd part of sum of divisors of n.
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2
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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; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 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.
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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.
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PROG
| (PARI) oddpart(n)=n/2^valuation(n, 2)
a(n)=oddpart(sigma(n))
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CROSSREFS
| Cf. A000265, A000203, A000593
Sequence in context: A130330 A050227 A135540 * A053092 A115873 A083239
Adjacent sequences: A161939 A161940 A161941 * A161943 A161944 A161945
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KEYWORD
| easy,mult,nonn
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AUTHOR
| Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Jun 22 2009
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