The number 2016 has 36 factors. Each factor, n, will lead to a sequence except for n=1.
Sum=(n/2)(2*a1+(n1)d
2016=(n/2)(2*a1+(n1)*2)
2016=n(a1+n1)
For each factor, solve for the first term a1
a1 = 2016/n  n + 1
and the rest follows
n=2, 1007+1009
n=3, 670+672+674
...
n=42, 7+9+11+...+49
n=48, 5+3+1+...+89
...
n=1008, 1005+1003+1002+...+1009
n=2016, 2014+2012+2010+...+2016
35 sequences in all, 17 of just positive integers.
Edit:
Those sequences with only positive integers can have extra terms added to the front that sum to zero, including the n=1 case.
So that's 18 more sequences for 53 total.
ex. n=42, 5+3+1+1+3+5+7+...+49
Edited on January 23, 2015, 12:50 pm

Posted by Jer
on 20150123 12:45:52 