OFFSET
1,2
COMMENTS
In wanting to ensure the definition was not arbitrary, I initially thought that 1s had to stop the recursion. But as T. D. Noe showed me, this doesn't have to be the case: the 1s can be included in the recursion.
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = sigma(n) + sum_{d | n, d < n} a(d). [Charles R Greathouse IV, Dec 20 2011]
MATHEMATICA
hsTD[n_] := hsTD[n] = Module[{d = Divisors[n]}, Total[d] + Total[hsTD /@ Most[d]]]; Table[hsTD[n], {n, 100}] (* From T. D. Noe *)
PROG
(PARI) a(n)=sumdiv(n, d, if(d<n, d+a(d), n)) \\ Charles R Greathouse IV, Dec 20 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alonso del Arte, May 26 2011
STATUS
approved