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Search: id:A154349
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| A154349 |
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Sum of proper divisors minus the number of proper divisors of Motzkin number A001006(n). |
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+0
1
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| 0, 0, 0, 1, 2, 8, 18, 0, 34, 170, 1643, 3603, 0, 25118, 139063, 474559, 284490, 984006, 6536387, 24265729, 18678366, 96214018, 277799290, 1282283434, 2077807072, 1899874612, 19252363859, 44221482383, 1967547352, 29743945396, 1265868622
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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Note that, if a(n)<>0 then Motzkin number A001006(n) is a composite number (A002808), otherwise A001006(n) is a non-composite number (A008578). See A152770.
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FORMULA
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a(n) = A001065(A001006(n))-A032741(A001006(n)) = A152770(A001006(n)).
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MAPLE
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with(numtheory): M := proc (n) options operator, arrow: (sum((-1)^j*binomial(n+1, j)*binomial(2*n-3*j, n), j = 0 .. floor((1/3)*n)))/(n+1) end proc: seq(sigma(M(n))-M(n)-tau(M(n))+1, n = 0 .. 30); [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 12 2009]
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CROSSREFS
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Cf. A001006, A001065, A002808, A032741, A008578, A152770, A152981, A152982, A152983, A152988, A152990.
Sequence in context: A034972 A061150 A160189 this_sequence A073601 A051248 A063664
Adjacent sequences: A154346 A154347 A154348 this_sequence A154350 A154351 A154352
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KEYWORD
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nonn
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AUTHOR
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Omar E. Pol (info(AT)polprimos.com), Jan 07 2009
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EXTENSIONS
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Extended by Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 12 2009
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