A384231 Index of the largest odd noncomposite divisor in the list of divisors of n.

1, 1, 2, 1, 2, 3, 2, 1, 2, 3, 2, 3, 2, 3, 3, 1, 2, 3, 2, 4, 3, 3, 2, 3, 2, 3, 2, 4, 2, 4, 2, 1, 3, 3, 3, 3, 2, 3, 3, 4, 2, 5, 2, 4, 3, 3, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 3, 2, 5, 2, 3, 3, 1, 3, 5, 2, 4, 3, 4, 2, 3, 2, 3, 3, 4, 3, 5, 2, 4, 2, 3, 2, 6, 3, 3, 3, 5, 2, 4, 3, 4, 3, 3, 3, 3, 2, 3, 4, 4

Offset

1,3

Comments

a(n) = 1 if and only if n is a power of 2.

Links

Table of n, a(n) for n=1..100.

Example

For n = 30 the divisors of 30 are [1, 2, 3, 5, 6, 10, 15, 30] and the largest odd noncomposite divisor is 5 and 5 is its 4th divisor, so a(30) = 4.

Mathematica

a[n_] := Module[{m = n/2^IntegerExponent[n, 2]}, If[m == 1, 1, Position[Divisors[n], FactorInteger[m][[-1, 1]]][[1, 1]]]]; Array[a, 100] (* Amiram Eldar, May 29 2025 *)

Crossrefs

Companion of A383401.

Right border of A384234.

Cf. A006005 (odd noncomposite numbers).

Cf. A000079, A027750, A384232, A384233.

Sequence in context: A285200 A308567 A192099 * A193101 A100661 A088696

Adjacent sequences: A384228 A384229 A384230 * A384232 A384233 A384234

Keyword

nonn,easy

Author

Omar E. Pol, May 29 2025

Status

approved