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A317305
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Sum of divisors of the n-th number whose divisors increase by a factor of 2 or less.
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6
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1, 3, 7, 12, 15, 28, 31, 39, 42, 60, 56, 72, 63, 91, 90, 96, 124, 120, 120, 168, 127, 144, 195, 186, 224, 180, 234, 252, 217, 210, 280, 248, 360, 312, 255, 336, 336, 403, 372, 392, 378, 363, 480, 372, 546, 508, 399, 468, 465, 504, 434, 576, 600, 504, 504, 560, 546, 744, 728, 511
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OFFSET
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1,2
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COMMENTS
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Also consider the n-th number k with the property that the symmetric representation of sigma(k) has only one part. a(n) is the area of the diagram (see the example). For more information see A237593 and its related sequences.
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LINKS
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FORMULA
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EXAMPLE
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Illustration of initial terms (n = 1..13):
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a(n)
_ _ _ _ _ _ _ _ _ _ _ _ _
1 |_| | | | | | | | | | | | | | | | | | | | | | | |
3 |_ _|_| | | | | | | | | | | | | | | | | | | | | |
_ _| _|_| | | | | | | | | | | | | | | | | | | |
7 |_ _ _| _|_| | | | | | | | | | | | | | | | | |
_ _ _| _| _ _| | | | | | | | | | | | | | | | |
12 |_ _ _ _| _| _ _ _| | | | | | | | | | | | | | | |
_ _ _ _| | _| _ _| | | | | | | | | | | | | | |
15 |_ _ _ _ _| _| | _ _ _| | | | | | | | | | | | | |
| _| | _ _ _|_| | | | | | | | | | | |
| _ _| _| | _ _ _|_| | | | | | | | | |
_ _ _ _ _ _| | _| _| | _ _ _ _| | | | | | | | |
28 |_ _ _ _ _ _ _| _ _| _| _ _| | _ _ _ _ _| | | | | | | |
| _ _| _| _| | _ _ _ _| | | | | | |
| | | | _ _| | _ _ _ _ _| | | | | |
_ _ _ _ _ _ _ _| | _ _| _ _|_| | | _ _ _ _ _|_| | | |
31 |_ _ _ _ _ _ _ _ _| | _ _| _| _ _| | | _ _ _ _ _|_| |
_ _ _ _ _ _ _ _ _| | | | _| _ _| | | _ _ _ _ _ _|
39 |_ _ _ _ _ _ _ _ _ _| | _ _| _| _ _| _ _| | |
_ _ _ _ _ _ _ _ _ _| | | | | _| _ _| |
42 |_ _ _ _ _ _ _ _ _ _ _| | _ _ _| _| _| | _ _|
| | | _| _| |
| | _ _ _| | _| _|
_ _ _ _ _ _ _ _ _ _ _ _| | | _ _ _| _ _| _|
60 |_ _ _ _ _ _ _ _ _ _ _ _ _| | | | _ _|
| | _ _ _| |
| | | _ _ _|
_ _ _ _ _ _ _ _ _ _ _ _ _ _| | | |
56 |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _| | |
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _| | |
72 |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _| |
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _| |
63 |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _|
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The length of the largest Dyck path of the n-th diagram equals A047836(n).
a(n) is the area of the n-th diagram.
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MATHEMATICA
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A317305[upto_]:=Table[If[AllTrue[Map[Last[#]/First[#]&, Partition[Divisors[n], 2, 1]], #<=2&], DivisorSigma[1, n], Nothing], {n, upto}];
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CROSSREFS
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Cf. A000203, A047836, A196020, A236104, A235791, A237048, A237591, A237593, A237270, A237271, A239660, A239931, A239932, A239933, A239934, A244050, A245092, A262626, A361208.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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