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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
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
KEYWORD
nonn,tabf,easy
AUTHOR
Paolo Xausa, Aug 18 2024
STATUS
approved