A361824 Sum of odd middle divisors of n, where "middle divisor" means a divisor in the half-open interval [sqrt(n/2), sqrt(n*2)).
1, 1, 0, 0, 0, 3, 0, 0, 3, 0, 0, 3, 0, 0, 8, 0, 0, 3, 0, 5, 0, 0, 0, 0, 5, 0, 0, 7, 0, 5, 0, 0, 0, 0, 12, 0, 0, 0, 0, 5, 0, 7, 0, 0, 14, 0, 0, 0, 7, 5, 0, 0, 0, 9, 0, 7, 0, 0, 0, 0, 0, 0, 16, 0, 0, 11, 0, 0, 0, 7, 0, 9, 0, 0, 0, 0, 18, 0, 0, 0, 9, 0, 0, 7, 0, 0, 0, 11, 0, 9, 20, 0, 0, 0, 0, 0, 0, 7, 20, 0
Offset: 1
Examples
For n = 8 the middle divisor of 8 is [2]. There are no odd middle divisors of 8 so a(8) = 0. For n = 12 the middle divisors of 12 are [3, 4]. There is only one odd middle divisor of 12 so a(12) = 3. For n = 15 the middle divisors of 15 are [3, 5]. There are two odd middle divisors of 15 so a(15) = 3 + 5 = 8.
Links
- Winston de Greef, Table of n, a(n) for n = 1..10000
- Michael De Vlieger, Log log scatterplot of a(n), n = 1..2^16.
- Michael De Vlieger, Detail of scalar scatterplot of a(n), n = 1..2^16, a(n) <= 384.
Crossrefs
Programs
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Mathematica
Table[Total@ Select[Divisors[n], And[Sqrt[n/2] <= # < Sqrt[2 n], OddQ[#] ] &], {n, 100}] (* Michael De Vlieger, Mar 27 2023 *) -
PARI
a(n) = vecsum(select(x->((x >= sqrt(n/2)) && (x < sqrt(n*2)) && x%2), divisors(n))); \\ Michel Marcus, Mar 26 2023
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