A377377 a(n) is the quotient of the practical number A005153(n) divided by its largest divisor that is primitive practical.

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, 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, 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

Offset

1,3

Comments

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.

Links

Frank M Jackson, Table of n, a(n) for n = 1..10000

Example

a(13) = 16 because the practical number A005153(13) = 32 = 2*16 and 2 is its largest primitive practical factor.
a(14) = 6 because the practical number A005153(14) = 36 = 6*6 and 6 is its largest primitive practical factor.

Mathematica

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}]

Crossrefs

Cf. A005153, A267124.

Sequence in context: A113418 A117000 A082392 * A233327 A307107 A085086

Adjacent sequences: A377365 A377366 A377367 * A377379 A377380 A377384

Keyword

nonn,new

Author

Frank M Jackson, Oct 26 2024

Status

approved