A114032 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 n-th group sum divided by n.

1, 17, 7, 7, 56, 161, 30, 95, 1020, 271, 90, 802, 1452, 790, 161, 7481, 309, 5882, 8400, 980, 10260, 6850, 11152, 6081, 15903, 3589, 18221, 2023, 32166, 32805, 9926, 110565, 18518, 4114, 29188, 4225, 83902, 47859, 70552, 89332, 37916, 93302, 34920

Offset

1,2

Links

Table of n, a(n) for n=1..43.

Formula

A114031(n)/n.

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: A114032 := proc(n) A114031(n)/n ; end: for n from 1 to 80 do printf("%d, ", A114032(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}]/n], strt += len]]];
Table[a[n], {n, 1, 43}] (* Jean-François Alcover, Aug 01 2023, after R. J. Mathar *)

Crossrefs

Cf. A114032, A114033.

Sequence in context: A166211 A086763 A064545 * A107807 A075710 A356060

Adjacent sequences: A114029 A114030 A114031 * A114033 A114034 A114035

Keyword

nonn

Author

Amarnath Murthy, Nov 13 2005

Extensions

More terms from R. J. Mathar, May 10 2007

Status

approved