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A109709 Triangle in which n-th row gives the prime factors of the n-th composite number with repetition.

%I A109709 #16 Apr 02 2024 15:54:28
%S A109709 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 A109709 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 A109709 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 A109709 Triangle in which n-th row gives the prime factors of the n-th composite number with repetition.
%e A109709 Irregular triangle begins:
%e A109709   2, 2;
%e A109709   2, 3;
%e A109709   2, 2, 2;
%e A109709   3, 3;
%e A109709   2, 5;
%e A109709   ...
%t A109709 fn[{a_,b_}]:=Table[a,b];Flatten[Table[fn/@FactorInteger[ ResourceFunction["Composite"][n]],{n,37}]] (* _James C. McMahon_, Mar 29 2024 *)
%Y A109709 Column k=1 gives A056608.
%Y A109709 Last terms in rows give A052369.
%Y A109709 Row lengths give A062502(n+1).
%Y A109709 Cf. A002808, A027746.
%K A109709 nonn,tabf
%O A109709 1,1
%A A109709 _Lior Manor_, Aug 08 2005