%I A085044
%S A085044 1,10,1,32,3,34,3,22,1,2,3,148,2,10,1,209,5,62,2,52,7,8,3,186,1,2,5,2,
               5,
%T A085044 138,2,4,11,6,17,324,2,7,5,86,5,78,3,28,11,8,11,402,15,62,15,2,2,6,9,34,
%U A085044 11,5,3,444,13,8,1,3905,3,6,2,2,7,14,3,348,13,2,3,2,27,2,3,370,49,6,2
%N A085044 Smallest number k such that tau(n) +tau(k) =tau(n+k), or 0 if no such 
               number exists.
%C A085044 Conjecture: No entry is zero. If n = p^2 where p is an odd prime then 
               a(n) < p^2 or a(n) = p^2 as tau(2p^2) = 6 = tau(p^2) + tau(p^2). 
               The (n,k) pairs are given below. (1,3),(2,10),(3,1),(4,841),(5,3),
               (6,66),(7,3),(8,37),(9,9),(10,2),(11,3),... Subsidiary sequence:(1) 
               members of this sequence such that a(n) = n. E.g. a(9) = 9. (2)(harder 
               one) Smallest k such that sigma(n) +sigma(k) = sigma(n+k).
%e A085044 a(8) = 22, as tau(8) = 4, tau(22) = 4 and tau(30) = 8 = tau(8)+tau(22).
%Y A085044 Sequence in context: A013617 A050999 A070246 this_sequence A059022 A115097 
               A050313
%Y A085044 Adjacent sequences: A085041 A085042 A085043 this_sequence A085045 A085046 
               A085047
%K A085044 nonn
%O A085044 1,2
%A A085044 Amarnath Murthy and Meenakshi Srikanth (amarnath_murthy(AT)yahoo.com), 
               Jun 19 2003
%E A085044 Corrected and extended by David Wasserman (wasserma(AT)spawar.navy.mil), 
               Jan 11 2005