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A361566
a(n) is the denominator of the median of divisors of n.
4
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
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
KEYWORD
nonn,frac
AUTHOR
Stefano Spezia, Mar 15 2023
STATUS
approved