A165897 - OEIS

A165897

a(n) = a(n-1) + largest proper divisor of a(n-1), a(1)=4.

%I #15 Apr 18 2016 02:59:06

%S 4,6,9,12,18,27,36,54,81,108,162,243,324,486,729,972,1458,2187,2916,

%T 4374,6561,8748,13122,19683,26244,39366,59049,78732,118098,177147,

%U 236196,354294,531441,708588,1062882,1594323,2125764,3188646,4782969

%N a(n) = a(n-1) + largest proper divisor of a(n-1), a(1)=4.

%H G. C. Greubel, <a href="/A165897/b165897.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,3).

%F a(1)=4, a(2)=6, a(3)=9, a(n) = 3*a(n-3) for n>3.

%F G.f.: x*(4+6*x+9*x^2) / ( 1-3*x^3 ). - _R. J. Mathar_, Nov 07 2015

%t NestList[ #+Divisors[ # ][[ -2]]&,4,50]

%t LinearRecurrence[{0, 0, 3}, {4, 6, 9}, 50] (* _G. C. Greubel_, Apr 17 2016 *)

%Y Cf. A000792.

%K nonn,easy

%O 1,1

%A _Zak Seidov_, Sep 29 2009