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A132065
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a(n) = Sum_{k=1 to d(n)} binomial(d(n)-1, k-1) d_k, where d(n) is the number of positive divisors of n and d_k is the k-th positive divisor of n (binomial(n,m) = n!/(m!(n-m)!)).
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1
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1, 3, 4, 9, 6, 22, 8, 27, 16, 32, 12, 123, 14, 42, 40, 81, 18, 164, 20, 171, 52, 62, 24, 704, 36, 72, 64, 219, 30, 808, 32, 243, 76, 92, 72, 1765, 38, 102, 88, 944, 42, 1016, 44, 315, 276, 122, 48, 4075, 64, 336, 112, 363, 54, 1224, 104, 1170, 124, 152, 60, 17815, 62
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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EXAMPLE
| Since the positive divisors of 12 are 1,2,3,4,6,12 and since row (d(12)-1) of Pascal's triangle is 1,5,10,10,5,1, a(12) = 1*1 + 5*2 + 10*3 + 10*4 + 5*6 + 1*12 = 123.
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MATHEMATICA
| f[n_] := Block[{d, l, k}, d = Divisors[n]; l = Length[d]; Sum[ Binomial[l - 1, k - 1]*d[[k]], {k, l}]]; Array[f, 100] (*Chandler*)
Table[Sum[Binomial[Length[Divisors[n]] - 1, k - 1]*Divisors[n][[k]], {k, 1, Length[Divisors[n]]}], {n, 1, 70}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Oct 31 2007
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CROSSREFS
| Sequence in context: A003959 A168341 A083111 * A157020 A180253 A055225
Adjacent sequences: A132062 A132063 A132064 * A132066 A132067 A132068
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KEYWORD
| nonn
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AUTHOR
| Leroy Quet Oct 30 2007
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EXTENSIONS
| Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net) and Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Nov 01 2007
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