A085044 Smallest number k such that tau(n) +tau(k) =tau(n+k), or 0 if no such number exists.

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

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: A221311 A361949 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