A369609 - OEIS

%I #52 Sep 27 2024 23:05:39

%S 1,2,3,2,4,5,6,7,2,4,8,3,9,10,11,6,12,13,14,15,2,4,8,16,17,6,12,18,19,

%T 10,20,21,22,23,6,12,18,24,5,25,26,3,9,27,14,28,29,30,31,2,4,8,16,32,

%U 33,34,35,6,12,18,24,36,37,38,39,10,20,40,41,42,43,22,44

%N Irregular triangle read by rows where row n lists k <= n such that A007947(k) = A007947(n).

%C Differs from A284318 after 27 terms.

%C Let rad(x) = A007947(x).

%C Let T(n,k) be the k-th term of row n in this sequence.

%C Define S(n,k) to be the k-th term in row n of A162306.

%C T(n,k) = rad(n) * S(n,k), k <= A008479(n).

%C The number n appears as the last term in row n.

%H Michael De Vlieger, <a href="/A369609/b369609.txt">Table of n, a(n) for n = 1..12946</a> (rows n = 1..5000, flattened)

%H Michael De Vlieger, <a href="/A369609/a369609.txt">Fast Mathematica programs that construct A008479, A010846, A162306, and A369609</a>

%F Row n of this sequence contains row n of A284318.

%F Length of row n is A008479(n).

%F For squarefree n, row n = {n}.

%F For prime power n = p^m, row n = { p^j : j = 1..m }.

%e First rows of the triangle:

%e   1;

%e   2;

%e   3;

%e   2, 4;

%e   5;

%e   6;

%e   7;

%e   2, 4, 8;

%e   3, 9;

%e   10;

%e   11;

%e   6, 12;

%e   13;

%e   14;

%e   15;

%e   2, 4, 8, 16;

%e   17;

%e   6, 12, 18;

%e   etc.

%t f[x_] := f[x] = Times @@ FactorInteger[x][[All, 1]]; Flatten@ Table[r = f[n]; Select[Range[n], f[#] == r &], {n, 44}]

%o (PARI) rad(n) = factorback(factorint(n)[, 1]); \\ A007947

%o row(n) = my(r=rad(n)); select(x->(rad(x) == r), [1..n]); \\ _Michel Marcus_, May 11 2024

%Y Cf. A007947, A008479, A162306, A284318.

%K nonn,tabf

%O 1,2

%A _Michael De Vlieger_, May 09 2024