A110353 -id:A110353 - cp's OEIS frontend

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

Amarnath Murthy, Jul 21 2005

nonn

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

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

Cf. A000217, A110352, A110353.

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

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  *)

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

A110352 A110351(n)/T(n) where T(n) is the n-th triangular number.

Original entry on oeis.org

2, 1, 5, 11, 2, 4, 41, 55, 13, 17, 7, 9, 32, 1, 26, 239, 59, 67, 14, 2, 12, 104, 60, 66, 137, 149, 46, 50, 23, 25, 929, 116, 20, 5, 39, 65, 314, 40, 6, 230, 34, 36, 117, 4, 82, 494, 219, 229, 563, 54, 27, 146, 662, 97, 9, 49, 91, 797, 220, 228, 884, 11, 740, 614, 18, 122, 251

Offset: 1

Amarnath Murthy, Jul 21 2005

nonn

Cf. A110351, A110353.

A110351 := proc(n) local k ; for k from 1 to n*(n+1) do if (k*(2*n+k+1)) mod (n*(n+1)) =0 then RETURN(k*(n+(k+1)/2)) ; fi ; od ; RETURN(0) ; end: A110352 := proc(n) 2*A110351(n)/(n*(n+1)) ; end: for n from 1 to 100 do printf("%d, ",A110352(n)) ; od ; # R. J. Mathar, May 02 2007

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*(n + 1))/2)], {n, 1, 60}] (* Stefan Steinerberger, Feb 17 2006 *)

More terms from Stefan Steinerberger, Feb 17 2006

More terms from R. J. Mathar, May 02 2007

cp's OEIS Frontend

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

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