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%I #21 Aug 29 2020 19:58:18
%S 0,1,2,2,2,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,
%T 7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,
%U 9,9,10,10,10,10,10,10,10,10,10,10,10,10,10
%N Least k such that sigma(1) + sigma(2) + sigma(3) +...+ sigma(k) >= n.
%H Alois P. Heinz, <a href="/A185283/b185283.txt">Table of n, a(n) for n = 0..100000</a> (terms n = 1..1000 from G. C. Greubel)
%e a(3) = 2 because sigma(1) + sigma(2) + sigma(3) = 1+3+4 > 3.
%p b:= proc(n) option remember; `if`(n=0, 0,
%p numtheory[sigma](n)+b(n-1))
%p end:
%p a:= proc(n) option remember; local k; for k from
%p `if`(n=0, 0, a(n-1)) do if b(k)>=n then return k fi od
%p end:
%p seq(a(n), n=0..120); # _Alois P. Heinz_, Sep 12 2019
%t a[n_] := (k = 1; While[ Total[ DivisorSigma[1, Range[k]]] < n, k++]; k); Table[ a[n], {n, 1, 90}]
%t Module[{nn=10,ad,th},ad={#[[1]],#[[2]]}&/@Partition[Accumulate[ DivisorSigma[ 1,Range[nn]]],2,1];th=Thread[{Range[2,nn],ad}];Join[ {0,1},Flatten[Table[#[[1]],#[[2,2]]-#[[2,1]]]&/@th]]] (* _Harvey P. Dale_, Aug 29 2020 *)
%Y Cf. A000203, A024916.
%K nonn
%O 0,3
%A _Michel Lagneau_, Jan 21 2012
%E a(0)=0 prepended by _Alois P. Heinz_, Sep 12 2019
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