|
%I #10 Aug 23 2014 14:58:18
%S 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,
%T 5,138,2,4,11,6,17,324,2,7,5,86,5,78,3,28,11,8,11,402,15,62,15,2,2,6,
%U 9,34,11,5,3,444,13,8,1,3905,3,6,2,2,7,14,3,348,13,2,3,2,27,2,3,370,49,6,2
%N Smallest number k such that tau(n) +tau(k) =tau(n+k), or 0 if no such number exists.
%C 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).
%H R. J. Mathar, <a href="/A085044/b085044.txt">Table of n, a(n) for n = 1..25199</a>
%e a(8) = 22, as tau(8) = 4, tau(22) = 4 and tau(30) = 8 = tau(8)+tau(22).
%K nonn
%O 1,2
%A _Amarnath Murthy_ and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 19 2003
%E Corrected and extended by _David Wasserman_, Jan 11 2005
|
