A383147 - OEIS

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

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OFFSET

1,6

LINKS

Table of n, a(n) for n=1..95.

FORMULA

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

EXAMPLE

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.

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 *)

CROSSREFS

Row sums of A383209.

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

Sequence in context: A035678 A094518 A383209 * A123074 A095269 A379461

Adjacent sequences: A383144 A383145 A383146 * A383148 A383149 A383150

KEYWORD

nonn

AUTHOR

Omar E. Pol, Apr 17 2025

STATUS

approved