A379698 Exponent of highest power of 2 that divides the n-th practical number A005153(n).

0, 1, 2, 1, 3, 2, 4, 1, 2, 3, 2, 1, 5, 2, 3, 1, 4, 1, 3, 2, 6, 1, 3, 1, 4, 2, 3, 1, 5, 2, 3, 2, 4, 3, 1, 7, 2, 2, 4, 1, 2, 5, 1, 3, 4, 2, 6, 2, 1, 3, 2, 4, 1, 3, 2, 5, 2, 1, 4, 2, 8, 2, 3, 1, 4, 2, 3, 5, 1, 2, 4, 1, 2, 3, 6, 2, 1, 4, 2, 1, 2, 5, 3, 2, 4, 1, 2, 7, 1, 3, 2, 4, 3, 1, 5, 2, 4, 3, 6, 1, 3, 2, 1, 4, 2, 2, 5, 1, 4, 2, 3, 1, 9, 3, 1, 4, 2, 2, 5, 1

Offset

1,3

Comments

The relationship between a practical number and highest power of 2 that divides it provides an equivalence relation. Practical numbers whose prime factorization have the same exponent of 2.

Links

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

Formula

a(n) = A007814(A005153(n)).

Example

a(9) = 2. A005153(9) = 20 and the greatest power of 2 that divides 20 is 2.

Mathematica

plst=Last/@ReadList["https://oeis.org/A005153/b005153.txt", {Number, Number}]; lst={}; Do[If[OddQ[plst[[n]]], AppendTo[lst, 0], AppendTo[lst, Last@First@FactorInteger[plst[[n]]]]], {n, 1, 100}]; lst

Crossrefs

Cf. A005153, A007814, A379325.

Sequence in context: A363489 A363944 A367581 * A323355 A367587 A363942

Adjacent sequences: A379695 A379696 A379697 * A379699 A379700 A379701

Keyword

nonn

Author

Frank M Jackson, Dec 30 2024

Status

approved