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

1,2

Comments

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

First differs from A325239 at row n = 8.

Links

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

Formula

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

Example

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;
  ...

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A100876 A089215 A238766 * A325239 A328739 A304088

Adjacent sequences: A375510 A375511 A375512 * A375514 A375515 A375516

Keyword

nonn,tabf,easy

Author

Paolo Xausa, Aug 18 2024

Status

approved