A072524 Sum of the remainders when the n-th triangular number is divided by all smaller triangular numbers > 1.

0, 0, 0, 5, 8, 10, 33, 35, 37, 86, 87, 122, 112, 207, 215, 255, 354, 389, 448, 493, 633, 710, 681, 1016, 1042, 1214, 1420, 1518, 1645, 1654, 2050, 2180, 2276, 2828, 2654, 3124, 3131, 3751, 3770, 4267, 4465, 4971, 5170, 5759, 6282, 6315, 6807, 7587, 7419

Offset

1,4

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

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.

Mathematica

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 *)

Prog

(PARI) for(n=1, 50, s=0; for(j=2, n-1, s=s+binomial(n+1, 2)%binomial(j+1, 2)); print1(s, ", "))

Crossrefs

Sequence in context: A314385 A185001 A057154 * A240968 A187878 A191233

Adjacent sequences: A072521 A072522 A072523 * A072525 A072526 A072527

Keyword

nonn

Author

Amarnath Murthy, Jul 31 2002

Extensions

Edited and extended by Klaus Brockhaus, Aug 02 2002

Status

approved