A375513 Irregular triangle read by rows in which row n lists the iterates of the sigma_0(x) map starting at n, until a fixed point is reached, where sigma_0(x) is the number-of-divisors function (A000005).

1, 2, 3, 2, 4, 3, 2, 5, 2, 6, 4, 3, 2, 7, 2, 8, 4, 3, 2, 9, 3, 2, 10, 4, 3, 2, 11, 2, 12, 6, 4, 3, 2, 13, 2, 14, 4, 3, 2, 15, 4, 3, 2, 16, 5, 2, 17, 2, 18, 6, 4, 3, 2, 19, 2, 20, 6, 4, 3, 2, 21, 4, 3, 2, 22, 4, 3, 2, 23, 2, 24, 8, 4, 3, 2, 25, 3, 2, 26, 4, 3, 2

Offset: 1

Author

Paolo Xausa, Aug 18 2024

Keywords

• nonn
• tabf
• easy

Comments

From the second row onward, the fixed point is 2.

First differs from A325239 at row n = 8.

Examples

			Triangle begins:
   1;
   2;
   3, 2;
   4, 3, 2;
   5, 2;
   6, 4, 3, 2;
   7, 2;
   8, 4, 3, 2;
   9, 3, 2;
  10, 4, 3, 2;
  11, 2;
  12, 6, 4, 3, 2;
  ...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000 (rows 1..2292 of triangle, flattened).

Crossrefs

Cf. A000005, A036459 (row lengths - 1), A060937 (row lengths, for n >= 2), A053477 (row sums), A325239.

Programs

Mathematica

Array[Most[FixedPointList[DivisorSigma[0, #] &, #]] &, 30]

PARI

row(n) = if (n==1, [1], my(list=List()); listput(list, n); while (n != 2, n = numdiv(n); listput(list, n)); Vec(list)); \\ Michel Marcus, Aug 21 2024

Formula

T(n,1) = n; T(n,k) = A000005(T(n,k-1)), for k = 2..A036459(n)+1.