%I A161942
%S A161942 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,
%T A161942 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,
%U A161942 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
%N A161942 Odd part of sum of divisors of n.
%C A161942 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.
%C A161942 Up to 20000000, there are only two odd numbers with a(n) and a(a(n)) 
               both >= n: 81 and 18966025.
%F A161942 Multiplicative with a(p^e) = oddpart((p^{e+1}-1)/(p-1)), where oddpart(n) 
               = A000265(n) is the largest odd divisor of n.
%o A161942 (PARI) oddpart(n)=n/2^valuation(n,2)
%o A161942 a(n)=oddpart(sigma(n))
%Y A161942 Cf. A000265, A000203, A000593
%Y A161942 Sequence in context: A130330 A050227 A135540 this_sequence A053092 A115873 
               A083239
%Y A161942 Adjacent sequences: A161939 A161940 A161941 this_sequence A161943 A161944 
               A161945
%K A161942 easy,mult,nonn
%O A161942 1,2
%A A161942 Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Jun 22 2009