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

Author

Omar E. Pol, May 14 2025

Keywords

• nonn
• easy

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.

Examples

			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.
		

Links

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

Crossrefs

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

Programs

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 *)

PARI

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

Formula

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