A383147 Sum of odd divisors m of n such that there is a divisor d of n with d < m < 2*d.

0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 3, 0, 0, 5, 0, 0, 12, 0, 5, 0, 0, 0, 3, 0, 0, 0, 7, 0, 23, 0, 0, 0, 0, 7, 12, 0, 0, 0, 5, 0, 31, 0, 0, 29, 0, 0, 3, 0, 0, 0, 0, 0, 39, 0, 7, 0, 0, 0, 23, 0, 0, 9, 0, 0, 47, 0, 0, 0, 7, 0, 12, 0, 0, 30, 0, 11, 42, 0, 5, 0, 0, 0, 31, 0, 0, 0, 11, 0, 77, 13, 0, 0, 0, 0

Offset: 1

Author

Omar E. Pol, Apr 17 2025

Keywords

• nonn

Examples

			For n = 18 there are two odd divisors m of 18 such that there is a divisor d of 18 with d < m < 2*d. Those odd divisors are 3 and 9 as shown below:
   d  <  m  <  2*d
--------------------
   1            2
   2     3      4
   3            6
   6     9     12
   9           18
  18           36
.
The sum of both divisors is 3 + 9 = 12, so a(18) = 12.
		

Crossrefs

Row sums of A383209.

Cf. A000593, A237270, A237271, A237593, A239657, A379379.

Programs

Mathematica

a[n_] := Module[{d = Partition[Divisors[n], 2, 1]}, Total[Select[d, OddQ[#[[2]]] && #[[2]] < 2*#[[1]] &][[;; , 2]]]]; Array[a, 100] (* Amiram Eldar, Apr 18 2025 *)

Formula

a(n) = A000593(n) - A379379(n).