%I A110351
%S A110351 2,3,30,110,30,84,1148,1980,585,935,462,702,2912,105,3120,32504,9027,
%T A110351 11457,2660,420,2772,26312,16560,19800,44525,52299,17388,20300,10005,
%U A110351 11625,460784,61248,11220,2975,24570,43290,220742,29640,4680,188600
%N A110351 Least sum (n+1) + (n+2) + ... + (n+k) which is a multiple of the n-th 
               triangular number n(n+1)/2.
%e A110351 a(3) = 4 + 5 + 6 + 7 + 8 = 30 = 5*6, T(3) = 3*4/2 = 6.
%p A110351 a:=proc(n) local p,m: p:=proc(k) if type(sum(n+j,j=1..k)/(n*(n+1)/2),
               integer)=true then k else fi end: m:=[seq(p(k),k=1..1200)][1]: sum(n+j,
               j=1..m) end: seq(a(n),n=1..45); (Deutsch)
%t A110351 Do[t = n*(n+1)/2; k = 1; While[Mod[k*n + k*(k+1)/2, t] > 0, k++ ]; Print[k*n 
               + k*(k+1)/2], {n, 1, 50}] (Propper)
%Y A110351 Cf. A110352, A110353.
%Y A110351 Sequence in context: A032814 A095927 A137981 this_sequence A088115 A048986 
               A093712
%Y A110351 Adjacent sequences: A110348 A110349 A110350 this_sequence A110352 A110353 
               A110354
%K A110351 nonn
%O A110351 1,1
%A A110351 Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jul 21 2005
%E A110351 More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu) and Ryan Propper 
               (rpropper(AT)stanford.edu), Aug 08 2005