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A339304
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Irregular triangle read by rows T(n,k) in which row n has length the partition number A000041(n-1) and columns k give the number of divisors function A000005, 1 <= k <= n.
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0
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1, 2, 2, 1, 3, 2, 1, 2, 2, 2, 1, 1, 4, 3, 2, 2, 2, 1, 1, 2, 2, 3, 2, 2, 2, 2, 1, 1, 1, 1, 4, 4, 2, 3, 3, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 3, 2, 4, 2, 2, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 4, 4, 2, 4, 4, 2, 2, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1
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OFFSET
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1,2
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COMMENTS
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T(n,k) is also the number of divisors of A336811(n,k).
Conjecture: the sum of row n equals A138137(n), the total number of parts in the last section of the set of partitions of n.
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LINKS
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Table of n, a(n) for n=1..97.
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FORMULA
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a(m) = A000005(A336811(m)).
T(n,k) = A000005(A336811(n,k).
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EXAMPLE
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Triangle begins:
1;
2;
2, 1;
3, 2, 1;
2, 2, 2, 1, 1;
4, 3, 2, 2, 2, 1, 1;
2, 2, 3, 2, 2, 2, 2, 1, 1, 1, 1;
4, 4, 2, 3, 3, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1;
3, 2, 4, 2, 2, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1;
...
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CROSSREFS
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Number of divisors of A336811.
Row n has length A000041(n-1).
Every column gives A000005.
Row sums give A138137 (conjectured).
Cf. A135010, A138121, A138879, A187219.
Sequence in context: A281013 A190683 A181810 * A237578 A026146 A325519
Adjacent sequences: A339301 A339302 A339303 * A339305 A339306 A339307
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KEYWORD
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nonn,tabf,new
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AUTHOR
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Omar E. Pol, Nov 29 2020
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STATUS
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approved
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