A361566 a(n) is the denominator of the median of divisors of n.

1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2

Offset

1,2

Comments

a(n) = 2 if n is in A139710, otherwise a(n) = 1. - Robert Israel, Mar 15 2023

Links

Winston de Greef, Table of n, a(n) for n = 1..10000

Index entries for sequences related to divisors of numbers

Formula

a(n) = denominator((A033676(n) + A033677(n))/2).

Except for p = 2 and k = 1, a(p^k) = 1, if p is a prime.

Example

a(9) = 1 since the divisors of 9 are 1, 3, 9, and their median is 3.
a(12) = 2 since the divisors of 12 are 1, 2, 3, 4, 6, 12, and their median is 7/2.

Mathematica

a[n_]:=Denominator[Median[Divisors[n]]]; Array[a, 88]

Prog

(PARI) a(n) = my(d=divisors(n), m=#d+1); denominator((d[m\2] + d[m-m\2])/2); \\ Michel Marcus, Mar 16 2023

Crossrefs

Cf. A027750, A033676, A033677, A071090, A139710, A139711, A361565 (numerator).

Sequence in context: A347441 A360617 A102097 * A354991 A354990 A318749

Adjacent sequences: A361563 A361564 A361565 * A361567 A361568 A361569

Keyword

nonn,frac

Author

Stefano Spezia, Mar 15 2023

Status

approved