login
A114031
Group the triangular numbers so that the n-th group sum is a multiple of n. 1, (3, 6, 10, 15), (21), (28), (36, 45, 55, 66, 78), (91, 105, 120, 136, 153, 171, 190), ... Sequence contains the group sums.
3
1, 34, 21, 28, 280, 966, 210, 760, 9180, 2710, 990, 9624, 18876, 11060, 2415, 119696, 5253, 105876, 159600, 19600, 215460, 150700, 256496, 145944, 397575, 93314, 491967, 56644, 932814, 984150, 307706, 3538080, 611094, 139876, 1021580, 152100
OFFSET
1,2
MAPLE
A000217 := proc(n) option remember ; n*(n+1)/2 ; end: A114031 := proc(n) local strt, su, len, i; strt := 1 ; for su from 1 to n do len := 1; while add( A000217(strt+i), i=0..len-1) mod su <> 0 do len := len+1 ; od ; if su = n then RETURN( add( A000217(strt+i), i=0..len-1) ) ; else strt := strt+len ; fi ; od ; end: for n from 1 to 80 do printf("%d, ", A114031(n)) ; od ; # R. J. Mathar, May 10 2007
MATHEMATICA
t[n_] := n(n+1)/2;
a[n_] := Module[{strt, su, len}, strt = 1; For[su = 1, True, su++, len = 1; While[Mod[Sum[t[strt+i], {i, 0, len-1}], su] != 0, len++]; If[su == n, Return[Sum[t[strt+i], {i, 0, len-1}]], strt += len]]];
Table[a[n], {n, 1, 36}] (* Jean-François Alcover, Aug 01 2023, after R. J. Mathar *)
CROSSREFS
Sequence in context: A033354 A033972 A298086 * A133733 A214038 A070727
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Nov 13 2005
EXTENSIONS
More terms from R. J. Mathar, May 10 2007
STATUS
approved