A383401 Index of the largest odd divisor in the list of divisors of n.

1, 1, 2, 1, 2, 3, 2, 1, 3, 3, 2, 3, 2, 3, 4, 1, 2, 5, 2, 4, 4, 3, 2, 3, 3, 3, 4, 4, 2, 7, 2, 1, 4, 3, 4, 6, 2, 3, 4, 4, 2, 7, 2, 4, 6, 3, 2, 3, 3, 5, 4, 4, 2, 7, 4, 4, 4, 3, 2, 9, 2, 3, 6, 1, 4, 7, 2, 4, 4, 7, 2, 7, 2, 3, 6, 4, 4, 7, 2, 4, 5, 3, 2, 9, 4, 3, 4, 5, 2, 11, 4, 4, 4, 3, 4, 3, 2, 5, 6, 7

Offset

1,3

Comments

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

a(n) = 2 if and only if n is an odd prime.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(2n-1) = A000005(2n-1).

Example

For n = 10 the divisors of 10 are [1, 2, 5, 10] and the largest odd divisor is 5 and 5 is the third divisor, so a(10) = 3.

Mathematica

a[n_] := If[OddQ[n], DivisorSigma[0, n], FirstPosition[Divisors[n], n/2^IntegerExponent[n, 2]][[1]]]; Array[a, 100] (* Amiram Eldar, May 14 2025 *)

Prog

(PARI) a(n) = select(x->x==n/2^valuation(n, 2), divisors(n), 1)[1]; \\ Michel Marcus, May 14 2025

Crossrefs

Cf. A000005, A000079, A000265, A001227, A027750, A065091, A174090.

Sequence in context: A293909 A002850 A355248 * A111944 A109814 A133088

Adjacent sequences: A383398 A383399 A383400 * A383402 A383403 A383404

Keyword

nonn,easy

Author

Omar E. Pol, May 14 2025

Status

approved