A361565 a(n) is the numerator of the median of divisors of n.

1, 3, 2, 2, 3, 5, 4, 3, 3, 7, 6, 7, 7, 9, 4, 4, 9, 9, 10, 9, 5, 13, 12, 5, 5, 15, 6, 11, 15, 11, 16, 6, 7, 19, 6, 6, 19, 21, 8, 13, 21, 13, 22, 15, 7, 25, 24, 7, 7, 15, 10, 17, 27, 15, 8, 15, 11, 31, 30, 8, 31, 33, 8, 8, 9, 17, 34, 21, 13, 17, 36, 17, 37, 39, 10

Offset

1,2

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) = numerator((A033676(n) + A033677(n))/2).

a(p) = (1 + p)/2 if p is an odd prime.

For p a prime, a(p^k) = (p^((k-1)/2) + p^((k+1)/2))/2 if k is odd, a(p^k) = p^(k/2) if k is even.

Example

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

Mathematica

a[n_]:=Numerator[Median[Divisors[n]]]; Array[a, 75]

Prog

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

Crossrefs

Cf. A027750, A033676, A033677, A071090, A139710, A139711, A361566 (denominator).

Sequence in context: A222666 A335401 A324465 * A334592 A248756 A059942

Adjacent sequences: A361562 A361563 A361564 * A361566 A361567 A361568

Keyword

nonn,frac

Author

Stefano Spezia, Mar 15 2023

Status

approved