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A126988
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Triangle read by rows: T(n,k) = n/k if k is a divisor of n; T(n,k) = 0 if k is not a divisor of n (1<=k<=n).
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52
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1, 2, 1, 3, 0, 1, 4, 2, 0, 1, 5, 0, 0, 0, 1, 6, 3, 2, 0, 0, 1, 7, 0, 0, 0, 0, 0, 1, 8, 4, 0, 2, 0, 0, 0, 1, 9, 0, 3, 0, 0, 0, 0, 0, 1, 10, 5, 0, 0, 2, 0, 0, 0, 0, 1, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 12, 6, 4, 3, 0, 2, 0, 0, 0, 0, 0, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Row sums = A000203 (sigma(n)): 1, 3, 4, 7, 6, 12, 8, 15,... sigma(n) is the sum of the divisors of the integer n. The sequence of parsed terms in sigma(n) is the reversal of non-zero row terms in the triangle A126988.
k-th column (k=0,1,2...) is (1,2,3,...) interspersed with n consecutive zeros starting after the "1".
The nonzero entries of row n are the divisors of n in decreasing order. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 17 2007
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REFERENCES
| David Wells, "Prime Numbers, the Most Mysterious Figures in Math", John Wiley & Sons, Inc, 2005, Appendix B.
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FORMULA
| G.f. of column k = z^k/(1-z^k)^2 (k=1,2,...). G.f.=G(t,z)=Sum(t^k*z^k/(1-z^k)^2,k=1..infinity). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 17 2007
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EXAMPLE
| First few rows of the triangle are:
1;
2, 1;
3, 0, 1;
4, 2, 0, 1;
5, 0, 0, 0, 1;
6, 3, 2, 0, 0, 1;
7, 0, 0, 0, 0, 0, 1;
8, 4, 0, 2, 0, 0, 0, 1;
9, 0, 3, 0, 0, 0, 0, 0, 1;
10, 5, 0, 0, 2, 0, 0, 0, 0, 1;
...
sigma(12) = 28 = (from tables): (1 + 2 + 3 + 4 + 6 + 12).
sigma(12) = 28, from 12-th row of A126988 = (12 + 6 + 4 + 3 + 2 + 1), deleting the zeros, from left to right.
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MAPLE
| A126988:=proc(n, k) if type(n/k, integer)=true then n/k else 0 fi end: for n from 1 to 12 do seq(A126988(n, k), k=1..n) od; # yields sequence in triangular form - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 17 2007
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MATHEMATICA
| t[n_, m_] = If[Mod[n, m] == 0, n/m, 0]; Table[Table[t[n, m], {m, 1, n}], {n, 1, 10}]; Flatten[%] - Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Sep 06 2008, simplified by Franklin T. Adams-Watters, Aug 24 2011
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CROSSREFS
| Cf. A000203.
Sequence in context: A158906 A143239 A158951 * A130026 A113287 A096798
Adjacent sequences: A126985 A126986 A126987 * A126989 A126990 A126991
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KEYWORD
| nonn,tabl
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 31 2006
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Jan 24 2007
Comment from Emeric Deutsch made name by Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Aug 24 2011
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