f&sub{k};(n) = &ref(): File not found: "p546_sigma1.png" at page "Problem 546"; f&sub{k};(⌊&sup{i};/&sub{k};⌋) と定義しよう, ここで f&sub{k};(0) = 1, そして ⌊x⌋ は床関数を表す.
例えば, f&sub{5};(10) = 18, f&sub{7};(100) = 1003, そして f&sub{2};(10&sup{3};) = 264830889564.
(&ref(): File not found: "p546_sigma2.png" at page "Problem 546"; f&sub{k};(10&sup{14};)) mod (10&sup{9};+7) を求めよ.