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A369609
Irregular triangle read by rows where row n lists k <= n such that A007947(k) = A007947(n).
4
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, 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, 33, 34, 35, 6, 12, 18, 24, 36, 37, 38, 39, 10, 20, 40, 41, 42, 43, 22, 44
OFFSET
1,2
COMMENTS
Differs from A284318 after 27 terms.
Let rad(x) = A007947(x).
Let T(n,k) be the k-th term of row n in this sequence.
Define S(n,k) to be the k-th term in row n of A162306.
T(n,k) = rad(n) * S(n,k), k <= A008479(n).
The number n appears as the last term in row n.
LINKS
FORMULA
Row n of this sequence contains row n of A284318.
Length of row n is A008479(n).
For squarefree n, row n = {n}.
For prime power n = p^m, row n = { p^j : j = 1..m }.
EXAMPLE
First rows of the triangle:
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;
etc.
MATHEMATICA
f[x_] := f[x] = Times @@ FactorInteger[x][[All, 1]]; Flatten@ Table[r = f[n]; Select[Range[n], f[#] == r &], {n, 44}]
PROG
(PARI) rad(n) = factorback(factorint(n)[, 1]); \\ A007947
row(n) = my(r=rad(n)); select(x->(rad(x) == r), [1..n]); \\ Michel Marcus, May 11 2024
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Michael De Vlieger, May 09 2024
STATUS
approved