A340791 -id:A340791 - cp's OEIS frontend

A340792 List in which n appears ceiling(d(n)/2) = A038548(n) times, where d(n) is the number of divisors of n.

1, 2, 3, 4, 4, 5, 6, 6, 7, 8, 8, 9, 9, 10, 10, 11, 12, 12, 12, 13, 14, 14, 15, 15, 16, 16, 16, 17, 18, 18, 18, 19, 20, 20, 20, 21, 21, 22, 22, 23, 24, 24, 24, 24, 25, 25, 26, 26, 27, 27, 28, 28, 28, 29, 30, 30, 30, 30, 31, 32, 32, 32, 33, 33, 34, 34, 35, 35, 36, 36, 36, 36, 36

Offset: 1

Charles Kusniec, Jan 21 2021

The numbers in A075362 arranged in numerical order.

			Array begins:
   1
   2
   3
   4  4
   5
   6  6
   7
   8  8
   9  9
  10 10
  11
  12 12 12
  13
  14 14
  15 15
  16 16 16
  17
  18 18 18
  19
  20 20 20
  21 21
  22 22
  23
  24 24 24 24

Charles Kusniec, Bijection between OEIS sequence A340792 and the positive Triangular Multiplication Table

Cf. A038548 (row lengths), A075362, A161906, A340791, A061017 (comparable array).

row(n) = my(d=divisors(n), r1=select(x->(x<=sqrt(n)), d), r2=Vecrev(select(x->(x>=sqrt(n)), d))); vector(#r1, k, r1[k]*r2[k]); \\ Michel Marcus, Jan 22 2021

T(n,k) = A161906(n,k) * A340791(n,k).

A319135 Irregular triangle read by rows in which row n lists the positive divisors of n that are <= sqrt(n) in decreasing order.

Original entry on oeis.org

1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 3, 1, 2, 1, 1, 3, 2, 1, 1, 2, 1, 3, 1, 4, 2, 1, 1, 3, 2, 1, 1, 4, 2, 1, 3, 1, 2, 1, 1, 4, 3, 2, 1, 5, 1, 2, 1, 3, 1, 4, 2, 1, 1, 5, 3, 2, 1, 1, 4, 2, 1, 3, 1, 2, 1, 5, 1, 6, 4, 3, 2, 1, 1, 2, 1, 3, 1, 5, 4, 2, 1, 1, 6, 3, 2, 1

Offset: 1

Charles Kusniec, Feb 27 2021

Reversing rows gives A161906.

			Triangle begins:
1
1
1
2 1
1
2 1
1
2 1
3 1
2 1
1
3 2 1
1
2 1
3 1
4 2 1

Cf. A038548 (row widths), A033676 (first column), A333750 (second column), A161906 (rows reversed), A027750, A056538, A061017, A340791, A340792.

row(n) = Vecrev(select(x->(x<=sqrt(n)), divisors(n))); \\ Jinyuan Wang, Mar 13 2021

a(n) * A161908(n) = A340792(n)
A161906(n) * A340791(n) = A340792(n)
A027750(n) * A056538(n) = A061017(n)

More terms from Jinyuan Wang, Mar 13 2021

cp's OEIS Frontend

A340792 List in which n appears ceiling(d(n)/2) = A038548(n) times, where d(n) is the number of divisors of n.

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