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A345116 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. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..94.

EXAMPLE

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.

CROSSREFS

Mirror of A110730.

Row lengths gives A000217, n >= 1.

Row sums gives A000292, n >= 1.

Every column gives A000027.

Cf. A000203, A175254, A237593, A245092, A333516, A340581.

Sequence in context: A343196 A016441 A340581 * A278042 A338714 A211161

Adjacent sequences:  A345113 A345114 A345115 * A345117 A345118 A345119

KEYWORD

nonn,tabf

AUTHOR

Omar E. Pol, Jun 08 2021

STATUS

approved

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Last modified August 3 22:03 EDT 2021. Contains 346441 sequences. (Running on oeis4.)