|
Search: id:A132065
|
|
|
| A132065 |
|
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)!)). |
|
+0
1
|
|
| 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; listen)
|
|
|
OFFSET
|
1,2
|
|
|
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.
|
|
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
|
|
CROSSREFS
|
Sequence in context: A084425 A003959 A083111 this_sequence A055225 A054791 A062319
Adjacent sequences: A132062 A132063 A132064 this_sequence A132066 A132067 A132068
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Leroy Quet (q1qq2qqq3qqqq(AT)yahoo.com), Oct 30 2007
|
|
EXTENSIONS
|
Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net) and Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Nov 01 2007
|
|
|
Search completed in 0.002 seconds
|
