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A010766
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Triangle of numbers [ n/k ], k=1..n.
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35
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1, 2, 1, 3, 1, 1, 4, 2, 1, 1, 5, 2, 1, 1, 1, 6, 3, 2, 1, 1, 1, 7, 3, 2, 1, 1, 1, 1, 8, 4, 2, 2, 1, 1, 1, 1, 9, 4, 3, 2, 1, 1, 1, 1, 1, 10, 5, 3, 2, 2, 1, 1, 1, 1, 1, 11, 5, 3, 2, 2, 1, 1, 1, 1, 1, 1, 12, 6, 4, 3, 2, 2, 1, 1, 1, 1, 1, 1, 13, 6, 4, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Number of times k occurs as divisor of numbers not greater than n. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 19 2004
Viewed as a partition, row n is the smallest partition that contains every partition of n. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Mar 11 2006
Row sums = A006218 - Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 30 2007
Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 30 2009: (Start)
A014668 = eigensequence of the triangle. A163313 = A010766 * A014668
(diagonalized) as an infinite lower triangular matrix) (End)
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LINKS
| T. D. Noe, Rows n=1..50 of triangle, flattened
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FORMULA
| G.f.: 1/(1-x)*Sum_(k>=1} x^k/(1-y*x^k). - Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 05 2004
Triangle A010766 = A000012 * A051731 as infinite lower triangular matrices. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 30 2007
Equals A000012 * A051731 as infinite lower triangular matrices. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 14 2007
Let T(n,0)=n+1, then T(n,k)=(sum of the k preceding elements in the previous column) minus (sum of the k preceding elements in same column). [From Mats Granvik, Gary W. Adamson (mats.granvik(AT)abo.fi), Feb 20 2010]
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EXAMPLE
| 1; 2,1; 3,1,1; 4,2,1,1; 5,2,1,1,1; ...
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CROSSREFS
| Another version of A003988.
Cf. A013942. Also ... A033330, ...
Cf. A006218, A115725.
T(n, 1)=n, T(n, 2)=A008619(n-2) for n>1, T(n, 3)=A008620(n-3) for n>2, T(n, 4)=A008621(n-4) for n>3, T(n, 5)=A002266(n) for n>4, T(n, n)=1.
Cf. A051731, A006218.
Cf. A051731, A000012.
A014668, A163313 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 30 2009]
Sequence in context: A088425 A141294 A174557 * A135841 A174066 A089178
Adjacent sequences: A010763 A010764 A010765 * A010767 A010768 A010769
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KEYWORD
| nonn,tabl,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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