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

Author

Stefano Spezia, Mar 15 2023

Keywords

• nonn
• frac

Examples

			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.
		

Links

• Winston de Greef, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to divisors of numbers

Crossrefs

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

Programs

Mathematica

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

PARI

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

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.