A185283 Least k such that sigma(1) + sigma(2) + sigma(3) +...+ sigma(k) >= n.

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, 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, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10

Offset: 0

Author

Michel Lagneau, Jan 21 2012

Keywords

• nonn

Examples

			a(3) = 2 because sigma(1) + sigma(2) + sigma(3) = 1+3+4 > 3.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..100000 (terms n = 1..1000 from G. C. Greubel)

Crossrefs

Cf. A000203, A024916.

Programs

Maple

b:= proc(n) option remember; `if`(n=0, 0,
       numtheory[sigma](n)+b(n-1))
    end:
a:= proc(n) option remember; local k; for k from
      `if`(n=0, 0, a(n-1)) do if b(k)>=n then return k fi od
    end:
seq(a(n), n=0..120);  # Alois P. Heinz, Sep 12 2019

Mathematica

a[n_] := (k = 1; While[ Total[ DivisorSigma[1, Range[k]]] < n, k++]; k); Table[ a[n], {n, 1, 90}]
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 *)

Formula

a(n) ~ c * sqrt(n), where c = 2*sqrt(3)/Pi. - Amiram Eldar, Dec 27 2024

Extensions

a(0)=0 prepended by Alois P. Heinz, Sep 12 2019