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Search: id:A085044
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| A085044 |
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Smallest number k such that tau(n) +tau(k) =tau(n+k), or 0 if no such number exists. |
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+0
1
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| 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
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OFFSET
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1,2
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COMMENT
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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).
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EXAMPLE
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a(8) = 22, as tau(8) = 4, tau(22) = 4 and tau(30) = 8 = tau(8)+tau(22).
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CROSSREFS
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Sequence in context: A013617 A050999 A070246 this_sequence A059022 A115097 A050313
Adjacent sequences: A085041 A085042 A085043 this_sequence A085045 A085046 A085047
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy and Meenakshi Srikanth (amarnath_murthy(AT)yahoo.com), Jun 19 2003
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EXTENSIONS
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Corrected and extended by David Wasserman (wasserma(AT)spawar.navy.mil), Jan 11 2005
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