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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).

%I A375513 #17 Sep 29 2024 21:11:03
%S A375513 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 A375513 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 A375513 2,22,4,3,2,23,2,24,8,4,3,2,25,3,2,26,4,3,2
%N 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).
%C A375513 From the second row onward, the fixed point is 2.
%C A375513 First differs from A325239 at row n = 8.
%H A375513 Paolo Xausa, <a href="/A375513/b375513.txt">Table of n, a(n) for n = 1..10000</a> (rows 1..2292 of triangle, flattened).
%F A375513 T(n,1) = n; T(n,k) = A000005(T(n,k-1)), for k = 2..A036459(n)+1.
%e A375513 Triangle begins:
%e A375513    1;
%e A375513    2;
%e A375513    3, 2;
%e A375513    4, 3, 2;
%e A375513    5, 2;
%e A375513    6, 4, 3, 2;
%e A375513    7, 2;
%e A375513    8, 4, 3, 2;
%e A375513    9, 3, 2;
%e A375513   10, 4, 3, 2;
%e A375513   11, 2;
%e A375513   12, 6, 4, 3, 2;
%e A375513   ...
%t A375513 Array[Most[FixedPointList[DivisorSigma[0, #] &, #]] &, 30]
%o A375513 (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 A375513 Cf. A000005, A036459 (row lengths - 1), A060937 (row lengths, for n >= 2), A053477 (row sums), A325239.
%K A375513 nonn,tabf,easy
%O A375513 1,2
%A A375513 _Paolo Xausa_, Aug 18 2024