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A345116
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Irregular triangle T(n,k) read by rows in which row n has length the n-th triangular number A000217(n) and every column k lists the positive integers A000027, n >= 1, k >= 1.
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2
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1, 2, 1, 1, 3, 2, 2, 1, 1, 1, 4, 3, 3, 2, 2, 2, 1, 1, 1, 1, 5, 4, 4, 3, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 6, 5, 5, 4, 4, 4, 3, 3, 3, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 7, 6, 6, 5, 5, 5, 4, 4, 4, 4, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 8, 7, 7, 6, 6, 6, 5, 5, 5, 5
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OFFSET
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1,2
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COMMENTS
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Row n lists the terms of the n-th row of A333516 in nonincreasing order.
The sum of the divisors of the terms of the n-th row of the triangle is equal to A175254(n), equaling the volume of the stepped pyramid with n levels described in A245092.
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LINKS
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EXAMPLE
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Triangle begins:
1;
2, 1, 1;
3, 2, 2, 1, 1, 1;
4, 3, 3, 2, 2, 2, 1, 1, 1, 1;
5, 4, 4, 3, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1;
6, 5, 5, 4, 4, 4, 3, 3, 3, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1;
...
For n = 6 the divisors of the terms of the 6th row of triangle are:
6, 5, 5, 4, 4, 4, 3, 3, 3, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1;
3, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1;
2, 1, 1, 1;
1;
The sum of these divisors is equal to A175254(6) = 82, equaling the volume of the stepped pyramid with six levels described in A245092.
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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