login
This site is supported by donations to The OEIS Foundation.

 

Logo

The OEIS is looking to hire part-time people to help edit core sequences, upload scanned documents, process citations, fix broken links, etc. - Neil Sloane, njasloane@gmail.com

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A161942 Odd part of sum of divisors of n. 9
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; text; internal format)
OFFSET

1,2

COMMENTS

It is conjectured that iteration of this function will always reach 1. This implies the nonexistence 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.

LINKS

Table of n, a(n) for n=1..82.

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.

MATHEMATICA

oddPart[n_] := n/2^IntegerExponent[n, 2]; a[n_] := oddPart[ DivisorSigma[1, n]]; Table[a[n], {n, 1, 82}] (* Jean-Fran├žois Alcover, Sep 03 2012 *)

PROG

(PARI)

oddpart(n)=n/2^valuation(n, 2);

a(n)=oddpart(sigma(n));

CROSSREFS

Cf. A000265, A000203, A000593

Sequence in context: A130330 A050227 A135540 * A247675 A053092 A212045

Adjacent sequences:  A161939 A161940 A161941 * A161943 A161944 A161945

KEYWORD

easy,mult,nonn

AUTHOR

Franklin T. Adams-Watters, Jun 22 2009

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified May 29 13:09 EDT 2017. Contains 287247 sequences.