A394673 Irregular triangle T(n, k), n > 0, k = 1..A282446(n), read by rows; the n-th row lists the recursive divisors of n (as defined in A282446).

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

Offset

1,3

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10005 (rows for n = 1..1476 flattened)

Rémy Sigrist, Illustration of initial terms

Index entries for sequences related to divisors

Formula

T(n, 1) = 1.

T(n, 2) = A020639(n) for any n > 1.

T(n, A282446(n)) = n.

Sum_{k = 1..A282446(n)} = A333926(n).

Example

Triangle T(n, k) begins:
  n   n-th row
  --  ------------------
   1  1
   2  1, 2
   3  1, 3
   4  1, 2, 4
   5  1, 5
   6  1, 2, 3, 6
   7  1, 7
   8  1, 2, 8
   9  1, 3, 9
  10  1, 2, 5, 10
  11  1, 11
  12  1, 2, 3, 4, 6, 12
  13  1, 13
  14  1, 2, 7, 14
  15  1, 3, 5, 15
  16  1, 2, 4, 16
  17  1, 17
  18  1, 2, 3, 6, 9, 18
  19  1, 19
  20  1, 2, 4, 5, 10, 20
.
See also Links section.

Prog

(PARI) A287957(n, k) = my (g=factor(gcd(n, k))); return (prod(i=1, #g~, g[i, 1]^A287957(valuation(n, g[i, 1]), valuation(k, g[i, 1]))))
row(n) = select(d -> A287957(n, d)==d, divisors(n))

Crossrefs

Cf. A020639, A282446, A333926 (row sums), A394674.

Sequence in context: A254679 A343651 A355634 * A275280 A379374 A319845

Adjacent sequences: A394669 A394670 A394671 * A394674 A394675 A394676

Keyword

nonn,tabf

Author

Rémy Sigrist, Mar 28 2026

Status

approved