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

Author

Frank M Jackson, Dec 30 2024

Keywords

• nonn

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.

Examples

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

Links

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

Crossrefs

Cf. A005153, A007814, A379325.

Programs

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

Formula

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