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A361650
Irregular triangle read by rows in which the row n lists the prime factors of n having the highest multiplicity.
0
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
2,1
COMMENTS
The row n has length A001221(n) iff n is squarefree or a perfect power.
EXAMPLE
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.
MATHEMATICA
r[n_]:=Commonest[Flatten[Table[#[[1]], {#[[2]]}] & /@ FactorInteger[n]]]; Flatten[Array[r, 58, 2]]
CROSSREFS
Cf. A001221, A001222, A027746, A051903, A356838 (1st column), A356840 (rightmost term), A361632, A361633.
Sequence in context: A100761 A336964 A027748 * A328852 A000705 A073751
KEYWORD
nonn,tabf
AUTHOR
Stefano Spezia, Mar 19 2023
STATUS
approved