cp's OEIS Frontend

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

%I A361650 #22 Mar 24 2023 07:59:29
%S A361650 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,
%T A361650 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,
%U A361650 3,2,23,47,2,7,5,3,17,2,53,3,5,11,2,3,19,2,29,59
%N A361650 Irregular triangle read by rows in which the row n lists the prime factors of n having the highest multiplicity.
%C A361650 The row n has length A001221(n) iff n is squarefree or a perfect power.
%e A361650 The triangle begins:
%e A361650    2;
%e A361650    3;
%e A361650    2;
%e A361650    5;
%e A361650    2, 3;
%e A361650    7;
%e A361650    2;
%e A361650    3;
%e A361650    2, 5;
%e A361650   11;
%e A361650    2;
%e A361650   13;
%e A361650    2, 7;
%e A361650    3, 5;
%e A361650    ...
%e A361650 The 12th row consists of {2} because 12 = 2*2*3, and the prime factor with the highest multiplicity is 2.
%e A361650 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.
%t A361650 r[n_]:=Commonest[Flatten[Table[#[[1]], {#[[2]]}] & /@ FactorInteger[n]]]; Flatten[Array[r,58,2]]
%Y A361650 Cf. A001221, A001222, A027746, A051903, A356838 (1st column), A356840 (rightmost term), A361632, A361633.
%K A361650 nonn,tabf
%O A361650 2,1
%A A361650 _Stefano Spezia_, Mar 19 2023