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 A085044 Smallest number k such that tau(n) +tau(k) =tau(n+k), or 0 if no such number exists. 1
 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, 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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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). LINKS R. J. Mathar, Table of n, a(n) for n = 1..25199 EXAMPLE a(8) = 22, as tau(8) = 4, tau(22) = 4 and tau(30) = 8 = tau(8)+tau(22). CROSSREFS Sequence in context: A223450 A221311 A070246 * A215268 A059022 A193634 Adjacent sequences:  A085041 A085042 A085043 * A085045 A085046 A085047 KEYWORD nonn AUTHOR Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 19 2003 EXTENSIONS Corrected and extended by David Wasserman, Jan 11 2005 STATUS approved

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Last modified December 15 09:05 EST 2019. Contains 329995 sequences. (Running on oeis4.)