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 A127013 Triangle read by rows: reversal of A126988. 6
 1, 1, 2, 1, 0, 3, 1, 0, 2, 4, 1, 0, 0, 0, 5, 1, 0, 0, 2, 3, 6, 1, 0, 0, 0, 0, 0, 7, 1, 0, 0, 0, 2, 0, 4, 8, 1, 0, 0, 0, 0, 0, 3, 0, 9, 1, 0, 0, 0, 0, 2, 0, 0, 5, 10, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 1, 0, 0, 0, 0, 0, 2, 0, 3, 4, 6, 12, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Let j = reversed indices of row terms. Then for any row, j*T(n,k) = n, for nonzero T(n,k). For example, in row 10, we match the terms with their j indices: (1, 0, 0, 0, 0, 2, 0, 0, 5, 10), (dot product) (10, 9, 8, 7, 6, 5, 4, 3, 2, 1); getting 10, 0, 0, 0, 0, 10, 0, 0, 10, 10). The factors of n are found in each row in order, as nonzero terms; e.g., 10 has the factors 1, 2, 5, 10, sum 18. Row sums = sigma(n), A000203. REFERENCES David Wells, "Prime Numbers, The Most Mysterious Figures in Math", John Wiley & Sons, 2005, Appendix. LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..7875 FORMULA Reversed rows of A126988. EXAMPLE First few rows of the triangle are:    1;    1, 2;    1, 0, 3;    1, 0, 2, 4;    1, 0, 0, 0, 5;    1, 0, 0, 2, 3, 6;    1, 0, 0, 0, 0, 0, 7;    1, 0, 0, 0, 2, 0, 4, 8;    1, 0, 0, 0, 0, 0, 3, 0, 9;    1, 0, 0, 0, 0, 2, 0, 0, 5, 10; Row 10 = (1, 0, 0, 0, 0, 2, 0, 0, 5, 10), reversal of 10th row of A126988. MATHEMATICA T[n_, m_]:= If[Mod[n, m]==0, n/m, 0]; Table[T[n, n-m+1], {n, 1, 12}, {m, 1, n}]//Flatten (* G. C. Greubel, Jun 03 2019 *) PROG (Haskell) a127013 n k = a127013_tabl !! (n-1) !! (k-1) a127013_row n = a127013_tabl !! (n-1) a127013_tabl = map reverse a126988_tabl -- Reinhard Zumkeller, Jan 20 2014 (PARI) {T(n, k) = if(n%k==0, n/k, 0)}; for(n=1, 12, for(k=1, n, print1(T(n, n-k+1), ", "))) \\ G. C. Greubel, Jun 03 2019 (MAGMA) [[(n mod (n-k+1)) eq 0 select n/(n-k+1) else 0: k in [1..n]]: n in [1..12]]; // G. C. Greubel, Jun 03 2019 (Sage) def T(n, k):     if (n%k==0): return n/k     else: return 0 [[T(n, n-k+1) for k in (1..n)] for n in (1..12)] # G. C. Greubel, Jun 03 2019 CROSSREFS Cf. A126988, A000203. Sequence in context: A120111 A130055 A202452 * A117362 A247492 A113214 Adjacent sequences:  A127010 A127011 A127012 * A127014 A127015 A127016 KEYWORD nonn,tabl AUTHOR Gary W. Adamson, Jan 02 2007 EXTENSIONS T(10,10) fixed by Reinhard Zumkeller, Jan 20 2014 More terms added by G. C. Greubel, Jun 03 2019 STATUS approved

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Last modified June 25 20:02 EDT 2022. Contains 354851 sequences. (Running on oeis4.)