Logic Masters Deutschland e.V.

The following puzzle is inspired from one mini puzzle in my latest pack.

Neighbors Sum has been sticking to my interest recently and while it delivers some interesting ideas for a puzzle, I feel like I want to extend the variant further so the variant will be much more flexible. Few weeks ago, I came up with an extension of the variant - Multiplied Neighbors Sum - and made a 6x6 puzzle out of it, and I actually liked how this one delivered in the solve path so I thought "cool, this has some good potentials there, let's try 9x9 next".
Compared to the small size like 6x6, 9x9 actually feels much more difficult to get into the variant's nature since the options are much more wider and I can very easily miss some unexpected cases. So ultimately, I'd like to make a fairly approachable 9x9 puzzle as the starter one. The difficulty should lie in the 3 range, I hope you enjoy the final result!



Rules:

- Normal Sudoku rules apply: every row, column and 3x3 box contains digits from 1 to 9 each once.

- Some cells contain a circle and a small number in their corner. If a digit is placed in such cell, the sum of all of its orthogonally adjacent cells must equal to the product of that digit and the respective small number in its corner (each adjacent cell is only counted once in the sum).
For example, if R2C1 is a 4 then the sum R1C1+R3C1+R2C2 will be 4x5 = 20.

A small note (highlight below to see if you want to know):

This puzzle can be solved without the given 7, for a harder challenge you can try to solve without it.

Puzzle:

F-puzzle link

Sudokulab (alt. link)

Penpa plus (alt. link)

CTC app (alt. link)

Good luck and have fun solving!