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A114033
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 number of terms in the n-th group.
3
1, 4, 1, 1, 5, 7, 1, 3, 17, 3, 1, 8, 11, 5, 1, 32, 1, 17, 19, 2, 19, 11, 16, 8, 19, 4, 19, 2, 29, 25, 7, 64, 9, 2, 14, 2, 37, 19, 26, 30, 12, 28, 10, 22, 1, 21, 3, 19, 49, 25, 17, 104, 53, 8, 11, 112, 19, 58, 29, 1, 61, 124, 35, 11, 9, 44, 8, 34, 46, 15, 69, 54, 73, 37, 1, 152, 77, 65
OFFSET
1,2
MAPLE
A000217 := proc(n) option remember ; n*(n+1)/2 ; end: A114033 := 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(len) ; else strt := strt+len ; fi ; od ; end: for n from 1 to 80 do printf("%d, ", A114033(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[len], strt += len]]];
Table[a[n], {n, 1, 78}] (* Jean-François Alcover, Aug 01 2023, after R. J. Mathar *)
CROSSREFS
Sequence in context: A174037 A173077 A131239 * A334426 A209417 A267990
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Nov 13 2005
EXTENSIONS
More terms from R. J. Mathar, May 10 2007
STATUS
approved