A110351 Least sum (n+1) + (n+2) + ... + (n+k) that is a multiple of the n-th triangular number, n(n+1)/2.

2, 3, 30, 110, 30, 84, 1148, 1980, 585, 935, 462, 702, 2912, 105, 3120, 32504, 9027, 11457, 2660, 420, 2772, 26312, 16560, 19800, 44525, 52299, 17388, 20300, 10005, 11625, 460784, 61248, 11220, 2975, 24570, 43290, 220742, 29640, 4680, 188600

Offset: 1

Author

Amarnath Murthy, Jul 21 2005

Keywords

• nonn

Examples

			a(3) = 4 + 5 + 6 + 7 + 8 = 30 = 5*6, T(3) = 3*4/2 = 6.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..250

Crossrefs

Cf. A000217, A110352, A110353.

Programs

Maple

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); # Emeric Deutsch, Aug 08 2005

Mathematica

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}] (* Ryan Propper, Aug 08 2005  *)

Extensions

More terms from Emeric Deutsch and Ryan Propper, Aug 08 2005