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%I #17 May 13 2013 01:54:20
%S 1,4,5,12,7,22,9,32,19,30,13,72,15,38,37,80,19,90,21,96,47,54,25,208,
%T 39,62,65,120,31,178,33,192,67,78,65,316,39,86,77,272,43,222,45,168,
%U 147,102,49,560,67,174,97,192,55
%N Hypersigma(n), definition 2: sum of the divisors of n plus the recursive sum of the divisors of the proper divisors.
%C 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.
%H Charles R Greathouse IV, <a href="/A191161/b191161.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = sigma(n) + sum_{d | n, d < n} a(d). [_Charles R Greathouse IV_, Dec 20 2011]
%t hsTD[n_] := hsTD[n] = Module[{d = Divisors[n]}, Total[d] + Total[hsTD /@ Most[d]]]; Table[hsTD[n], {n, 100}] (* From T. D. Noe *)
%o (PARI) a(n)=sumdiv(n,d,if(d<n,d+a(d),n)) \\ _Charles R Greathouse IV_, Dec 20 2011
%Y Cf. A000203, A191150.
%K nonn,easy
%O 1,2
%A _Alonso del Arte_, May 26 2011
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