login
a(0)=1; a(1)=1; for n >= 2, a(n) = a(n-1) + a(n-A000005(n)).
2

%I #28 Oct 16 2018 02:45:00

%S 1,1,2,3,4,7,9,16,20,29,38,67,76,143,181,248,315,563,639,1202,1383,

%T 1946,2585,4531,4846,7431,10016,14547,17132,31679,34264,65943,75959,

%U 107638,141902,207845,222392,430237,572139,779984,855943,1635927,1777829,3413756,3985895,4765879

%N a(0)=1; a(1)=1; for n >= 2, a(n) = a(n-1) + a(n-A000005(n)).

%H Vaclav Kotesovec, <a href="/A320357/b320357.txt">Table of n, a(n) for n = 0..9000</a>

%H Vaclav Kotesovec, <a href="/A320357/a320357.jpg">Graph a(n+1)/a(n)</a>

%F 1 <= a(n+1)/a(n) <= 2. - _Vaclav Kotesovec_, Oct 14 2018

%F By empirical observation a(n) ~ 3.179662855437*exp(0.3175*n). - _Ctibor O. Zizka_, Oct 15 2018

%e a(4) = a(3)+a(1) = a(2)+a(1)+a(1) = a(1)+a(0)+a(1)+a(1) = 4.

%t a[n_] := a[n] = If[n < 2, 1, a[n-1] + a[n - DivisorSigma[0, n]]]; Table[a[n], {n, 0, 50}] (* _Vaclav Kotesovec_, Oct 14 2018 *)

%Y Cf. A000005, A155043, A320520.

%K nonn

%O 0,3

%A _Ctibor O. Zizka_, Oct 11 2018