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Search: id:A055507
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| A055507 |
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Sum{k = 1 to n}[d(k)*d(n+1-k)], where d(k) is number of positive divisors of k. |
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+0
4
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| 1, 4, 8, 14, 20, 28, 37, 44, 58, 64, 80, 86, 108, 108, 136, 134, 169, 160, 198, 192, 236, 216, 276, 246, 310, 288, 348, 310, 400, 344, 433, 396, 474, 408, 544, 450, 564, 512, 614, 522, 688, 560, 716, 638, 756, 636, 860, 676, 859, 772, 926, 758, 1016, 804, 1032
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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a(n) = number of ways to express n+1 as a*b+c*d in positive integers a, b, c, d. - David W. Wilson (davidwwilson(AT)comcast.net), Jun 16 2003
tau(n) (A000005) convolved with itself, treating this result as a sequence whose offset is 2 - Graeme McRae (g_m(AT)mcraefamily.com), Jun 06 2006
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LINKS
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Leroy Quet, Home Page (listed in lieu of email address)
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FORMULA
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G.f.: Sum_{i >= 1, j >= 1} x^(i+j-1)/(1-x^i)/(1-x^j). - Vladeta Jovovic (vladeta(AT)eunet.rs), Nov 11 2001
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EXAMPLE
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a[4] = d(1)*d(4) +d(2)*d(3) +d(3)*d(2) +d(4)*d(1) = 1*3 +2*2 +2*2 +3*1 = 14
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CROSSREFS
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Cf. A000385.
Sequence in context: A067699 A066941 A049420 this_sequence A121896 A131937 A088804
Adjacent sequences: A055504 A055505 A055506 this_sequence A055508 A055509 A055510
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KEYWORD
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easy,nonn
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AUTHOR
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Leroy Quet Jun 29 2000
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jul 04 2000
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