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%I #8 Oct 14 2017 15:12:31
%S 0,0,0,5,8,10,33,35,37,86,87,122,112,207,215,255,354,389,448,493,633,
%T 710,681,1016,1042,1214,1420,1518,1645,1654,2050,2180,2276,2828,2654,
%U 3124,3131,3751,3770,4267,4465,4971,5170,5759,6282,6315,6807,7587,7419
%N Sum of the remainders when the n-th triangular number is divided by all smaller triangular numbers > 1.
%H Harvey P. Dale, <a href="/A072524/b072524.txt">Table of n, a(n) for n = 1..1000</a>
%e The eighth triangular number is 36; division by 3, 6, 10, 15,21, 28 gives the remainders 0, 0, 6, 6, 15, 8, so a(8) = 0 + 0 + 6+ 6 + 15 + 8 = 35.
%t sr[x_]:=Total[Mod[Last[x],x[[2;;Length[x]-1]]]]; Module[{nn=50,tr}, tr= Accumulate[ Range[nn]];Join[{0},Table[sr[Take[tr,n]],{n,2,nn}]]] (* _Harvey P. Dale_, Oct 14 2017 *)
%o (PARI) for(n=1,50,s=0; for(j=2,n-1,s=s+binomial(n+1,2)%binomial(j+1,2)); print1(s,","))
%K nonn
%O 1,4
%A _Amarnath Murthy_, Jul 31 2002
%E Edited and extended by _Klaus Brockhaus_, Aug 02 2002
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