A351752 Floor of the average of the numbers |x-y| over all pairs (x,y) with x*y = n, x <= y.

0, 1, 2, 1, 4, 3, 6, 4, 4, 6, 10, 5, 12, 9, 8, 7, 16, 9, 18, 9, 12, 15, 22, 10, 12, 18, 16, 14, 28, 12, 30, 16, 20, 24, 18, 13, 36, 27, 24, 16, 40, 18, 42, 23, 20, 33, 46, 18, 24, 25, 32, 28, 52, 24, 30, 23, 36, 42, 58, 21, 60, 45, 27, 26, 36, 30, 66, 37

Offset

1,3

Comments

Graph resembles that of Euler's totient function (A000010).

Links

Michel Marcus, Table of n, a(n) for n = 1..10000

Example

a(12) = floor(average of {12-1, 6-2, 4-3}) = 5.
a(16) = floor(average of {16-1, 8-2, 4-4}) = 7.

Mathematica

A351752[n_] := Floor[Mean[TakeWhile[Reverse[#] - #, NonNegative]]] & [Divisors[n]];
Array[A351752, 100] (* Paolo Xausa, Jan 16 2026 *)

Prog

(Python)
from sympy import divisors
def a(n):
    arr = divisors(n)
    length = (len(arr)+1)//2
    total = 0
    for i in range(length):
        total += arr[-(i+1)] - arr[i]
    return total // length
for i in range(1, 80):
    print("{}, ".format(a(i)), end="")
(PARI) a(n) = my(v=divisors(n)); vecsum(abs(v-Vecrev(v))) \ (#v + #v%2); \\ Kevin Ryde, Mar 10 2022

Crossrefs

Cf. A000010, A027750.

Sequence in context: A338657 A347082 A186421 * A361189 A004560 A345668

Adjacent sequences: A351749 A351750 A351751 * A351753 A351754 A351755

Keyword

nonn,easy

Author

Christoph B. Kassir, Mar 09 2022

Status

approved