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%I #11 Aug 01 2023 07:34:49
%S 1,34,21,28,280,966,210,760,9180,2710,990,9624,18876,11060,2415,
%T 119696,5253,105876,159600,19600,215460,150700,256496,145944,397575,
%U 93314,491967,56644,932814,984150,307706,3538080,611094,139876,1021580,152100
%N 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.
%p 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
%t t[n_] := n(n+1)/2;
%t 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]]];
%t Table[a[n], {n, 1, 36}] (* _Jean-François Alcover_, Aug 01 2023, after _R. J. Mathar_ *)
%Y Cf. A114032, A114033.
%K nonn
%O 1,2
%A _Amarnath Murthy_, Nov 13 2005
%E More terms from _R. J. Mathar_, May 10 2007
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