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A378202 Largest primitive practical number that divides the n-th practical number - A005153(n).

%I A378202 #6 Nov 20 2024 09:51:22
%S A378202 1,2,2,6,2,6,2,6,20,6,28,30,2,6,20,42,6,6,28,30,2,66,6,78,20,42,88,30,
%T A378202 6,20,104,6,28,30,42,2,66,140,6,30,78,20,6,42,88,30,6,28,66,20,204,
%U A378202 104,210,6,220,28,228,78,30,42,2,260,88,30,272,276,140,6,42,30,304,306,308,104,20,6,330,42,340,342,348,88,30,364,368,42,380,6,390,28,66
%N A378202 Largest primitive practical number that divides the n-th practical number - A005153(n).
%C A378202 Every practical number has a primitive practical divisor. a(n) is the largest primitive practical number that divides A005153(n). The quotient of A005153(n)/a(n) is A377377(n).
%e A378202 a(8) = 6 because A005153(8) = 18 and the largest primitive practical that divides 18 is 6.
%t A378202 plst=Last/@ReadList["https://oeis.org/A005153/b005153.txt", {Number, Number}]; pplst=Last/@ReadList["https://oeis.org/A267124/b267124.txt", {Number, Number}]; getpplst[n_] := Module[{}, Select[pplst, #<=n &]]; lst1={}; Do[lst=getpplst[plst[[n]]]; lnh=Length@lst; m = 0; While[!IntegerQ[j=plst[[n]]/(k=lst[[lnh-m]])], m++]; AppendTo[lst1, {k, j}], {n, 1, 100}]; First/@lst1
%Y A378202 Cf. A005153, A267124, A377377.
%K A378202 nonn
%O A378202 1,2
%A A378202 _Frank M Jackson_, Nov 19 2024