cp's OEIS Frontend

A369609 Irregular triangle read by rows where row n lists k <= n such that A007947(k) = A007947(n).

%I A369609 #52 Sep 27 2024 23:05:39
%S A369609 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 A369609 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 A369609 33,34,35,6,12,18,24,36,37,38,39,10,20,40,41,42,43,22,44
%N A369609 Irregular triangle read by rows where row n lists k <= n such that A007947(k) = A007947(n).
%C A369609 Differs from A284318 after 27 terms.
%C A369609 Let rad(x) = A007947(x).
%C A369609 Let T(n,k) be the k-th term of row n in this sequence.
%C A369609 Define S(n,k) to be the k-th term in row n of A162306.
%C A369609 T(n,k) = rad(n) * S(n,k), k <= A008479(n).
%C A369609 The number n appears as the last term in row n.
%H A369609 Michael De Vlieger, <a href="/A369609/b369609.txt">Table of n, a(n) for n = 1..12946</a> (rows n = 1..5000, flattened)
%H A369609 Michael De Vlieger, <a href="/A369609/a369609.txt">Fast Mathematica programs that construct A008479, A010846, A162306, and A369609</a>
%F A369609 Row n of this sequence contains row n of A284318.
%F A369609 Length of row n is A008479(n).
%F A369609 For squarefree n, row n = {n}.
%F A369609 For prime power n = p^m, row n = { p^j : j = 1..m }.
%e A369609 First rows of the triangle:
%e A369609   1;
%e A369609   2;
%e A369609   3;
%e A369609   2, 4;
%e A369609   5;
%e A369609   6;
%e A369609   7;
%e A369609   2, 4, 8;
%e A369609   3, 9;
%e A369609   10;
%e A369609   11;
%e A369609   6, 12;
%e A369609   13;
%e A369609   14;
%e A369609   15;
%e A369609   2, 4, 8, 16;
%e A369609   17;
%e A369609   6, 12, 18;
%e A369609   etc.
%t A369609 f[x_] := f[x] = Times @@ FactorInteger[x][[All, 1]]; Flatten@ Table[r = f[n]; Select[Range[n], f[#] == r &], {n, 44}]
%o A369609 (PARI) rad(n) = factorback(factorint(n)[, 1]); \\ A007947
%o A369609 row(n) = my(r=rad(n)); select(x->(rad(x) == r), [1..n]); \\ _Michel Marcus_, May 11 2024
%Y A369609 Cf. A007947, A008479, A162306, A284318.
%K A369609 nonn,tabf
%O A369609 1,2
%A A369609 _Michael De Vlieger_, May 09 2024