%I #14 Apr 22 2024 19:08:18

%S 1,3,24,48,72,96,120,144,192,216,240,288,336,360,384,406,432,480,576,

%T 600,648,672,720,768,864,936,960,1008,1080,1104,1152,1200,1224,1296,

%U 1320,1344,1368,1440,1536,1680,1728,1800,1920,1944,2016,2160,2208,2304

%N Numbers k such that the arithmetic mean of the first k Lucas numbers A000032 is an integer.

%C Numbers n such that sum(i=0..n, A000032(i))/(n+1) is an integer. - _Robert G. Wilson v_, May 25 2009

%C Why do the terms in A141767 so closely correspond to A160665? Except for n = 1, 3, 406, 44758, 341446, 1413286, 3170242, 4861698, 7912534, ..., n == 0 (mod 24). - _Robert G. Wilson v_, May 25 2009

%F {n: n | A001610(n)}. - _R. J. Mathar_, May 25 2009

%p A000032 := proc(n) option remember ; if n <= 1 then 2-n; else procname(n-1)+procname(n-2) ; fi; end: A001610 := proc(n) add(A000032(i),i=0..n-1) ; end: for n from 1 to 3000 do if A001610(n) mod n = 0 then printf("%d,",n) ; fi; od: # _R. J. Mathar_, May 25 2009

%t lst = {}; a = 2; b = 1; s = 3; n = 3; While[n < 2447, c = a + b; s = s + c; If[Mod[c, n] == 0, AppendTo[lst, n]]; a = b; b = c; n++ ]; lst (* _Robert G. Wilson v_, May 25 2009 *)

%Y Cf. A000032, A111058, A140826, A140971, A140972.

%K nonn

%O 1,2

%A _Ctibor O. Zizka_, May 22 2009

%E More terms from _R. J. Mathar_ and _Robert G. Wilson v_, May 25 2009