A361650 Irregular triangle read by rows in which the row n lists the prime factors of n having the highest multiplicity.

2, 3, 2, 5, 2, 3, 7, 2, 3, 2, 5, 11, 2, 13, 2, 7, 3, 5, 2, 17, 3, 19, 2, 3, 7, 2, 11, 23, 2, 5, 2, 13, 3, 2, 29, 2, 3, 5, 31, 2, 3, 11, 2, 17, 5, 7, 2, 3, 37, 2, 19, 3, 13, 2, 41, 2, 3, 7, 43, 2, 3, 2, 23, 47, 2, 7, 5, 3, 17, 2, 53, 3, 5, 11, 2, 3, 19, 2, 29, 59

Offset: 2

Author

Stefano Spezia, Mar 19 2023

Keywords

• nonn
• tabf

Comments

The row n has length A001221(n) iff n is squarefree or a perfect power.

Examples

			The triangle begins:
   2;
   3;
   2;
   5;
   2, 3;
   7;
   2;
   3;
   2, 5;
  11;
   2;
  13;
   2, 7;
   3, 5;
   ...
The 12th row consists of {2} because 12 = 2*2*3, and the prime factor with the highest multiplicity is 2.
The 30th row consists of {2, 3, 5} because 30 = 2*3*5, and the prime factors with the highest multiplicity are 2, 3, and 5.
		

Crossrefs

Cf. A001221, A001222, A027746, A051903, A356838 (1st column), A356840 (rightmost term), A361632, A361633.

Programs

Mathematica

r[n_]:=Commonest[Flatten[Table[#[[1]], {#[[2]]}] & /@ FactorInteger[n]]]; Flatten[Array[r,58,2]]