A375513 - OEIS

%I #17 Sep 29 2024 21:11:03

%S 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,

%T 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,

%U 2,22,4,3,2,23,2,24,8,4,3,2,25,3,2,26,4,3,2

%N 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).

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

%C First differs from A325239 at row n = 8.

%H Paolo Xausa, <a href="/A375513/b375513.txt">Table of n, a(n) for n = 1..10000</a> (rows 1..2292 of triangle, flattened).

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

%e Triangle begins:

%e    1;

%e    2;

%e    3, 2;

%e    4, 3, 2;

%e    5, 2;

%e    6, 4, 3, 2;

%e    7, 2;

%e    8, 4, 3, 2;

%e    9, 3, 2;

%e   10, 4, 3, 2;

%e   11, 2;

%e   12, 6, 4, 3, 2;

%e   ...

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

%o (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

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

%K nonn,tabf,easy

%O 1,2

%A _Paolo Xausa_, Aug 18 2024