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Triangle in which n-th row gives the prime factors of the n-th composite number with repetition.
0

%I #16 Apr 02 2024 15:54:28

%S 2,2,2,3,2,2,2,3,3,2,5,2,2,3,2,7,3,5,2,2,2,2,2,3,3,2,2,5,3,7,2,11,2,2,

%T 2,3,5,5,2,13,3,3,3,2,2,7,2,3,5,2,2,2,2,2,3,11,2,17,5,7,2,2,3,3,2,19,

%U 3,13,2,2,2,5,2,3,7,2,2,11,3,3,5,2,23,2,2,2,2,3,7,7,2,5,5,3,17,2,2,13,2,3,3,3

%N Triangle in which n-th row gives the prime factors of the n-th composite number with repetition.

%e Irregular triangle begins:

%e 2, 2;

%e 2, 3;

%e 2, 2, 2;

%e 3, 3;

%e 2, 5;

%e ...

%t fn[{a_,b_}]:=Table[a,b];Flatten[Table[fn/@FactorInteger[ ResourceFunction["Composite"][n]],{n,37}]] (* _James C. McMahon_, Mar 29 2024 *)

%Y Column k=1 gives A056608.

%Y Last terms in rows give A052369.

%Y Row lengths give A062502(n+1).

%Y Cf. A002808, A027746.

%K nonn,tabf

%O 1,1

%A _Lior Manor_, Aug 08 2005