A377377 - OEIS

%I #15 Nov 03 2024 19:33:14

%S 1,1,2,1,4,2,8,3,1,4,1,1,16,6,2,1,8,9,2,2,32,1,12,1,4,2,1,3,16,5,1,18,

%T 4,4,3,64,2,1,24,5,2,8,27,4,2,6,32,7,3,10,1,2,1,36,1,8,1,3,8,6,128,1,

%U 3,9,1,1,2,48,7,10,1,1,1,3,16,54,1,8,1,1,1,4,12,1,1,9,1,64,1,14,6,20,2,1,4,2,72,2,16,15,2,1,1,1,6,1,16,81,1,25,12

%N a(n) is the quotient of the practical number A005153(n) divided by its largest divisor that is primitive practical.

%C Every practical number > 1 contains at least one primitive practical divisor because they are all even and 2 is primitive practical. Also 1 is primitive practical. If the largest primitive practical factor of the practical number A005153(n) is p then a(n)*p = A005153(n). Whenever a(n) = 1, A005153(n) is also primitive practical.

%H Frank M Jackson, <a href="/A377377/b377377.txt">Table of n, a(n) for n = 1..10000</a>

%e a(13) = 16 because the practical number A005153(13) = 32 = 2*16 and 2 is its largest primitive practical factor.

%e a(14) = 6 because the practical number A005153(14) = 36 = 6*6 and 6 is its largest primitive practical factor.

%t lst1=Last/@ReadList["https://oeis.org/A267124/b267124.txt", {Number, Number}]; lst2=Last/@ReadList["https://oeis.org/A005153/b005153.txt", {Number, Number}]; getm[p_] := Module[{plst=Select[lst1, #<=p &], k, l, n=0}, l=Length@plst; If[Last@plst==p, Return[1]]; While[!IntegerQ[k=p/plst[[l-n]]], n++]; k]; Table[getm[lst2[[n]]], {n, 1, 100}]

%Y Cf. A005153, A267124.

%K nonn

%O 1,3

%A _Frank M Jackson_, Oct 26 2024