

A161942


Odd part of sum of divisors of n.


2



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
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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)/(p1)), 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}] (* JeanFrançois 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. AdamsWatters, Jun 22 2009


STATUS

approved



