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This property of multiplicative functions significantly reduces the need for computation, as in the following examples for ''n'' = 144 = 2<sup>4</sup> · 3<sup>2</sup>:
{{block<math indent|emdisplay =1.2|text= "block"> d(144) = ''σ''<sub>0</sub>\sigma_0 (144) = ''σ''<sub>0</sub>\sigma_0 (2<sup>^ 4</sup>)''σ''<sub>0</sub> \, \sigma_0 (3<sup>^ 2</sup>) = (1<sup>^ 0</sup> + 2<sup>^ 0</sup> + 4<sup>^ 0</sup> + 8<sup>^ 0</sup> + 16<sup>^ 0</sup>)(1<sup>^ 0</sup> + 3<sup>^ 0</sup> + 9<sup>^ 0</sup>) = 5 ·\cdot 3 = 15,}}</math>
{{block<math indent|emdisplay =1.2|text= ''σ''"block">\sigma (144) = ''σ''<sub>1</sub>\sigma_1 (144) = ''σ''<sub>1</sub>\sigma_1 (2<sup>^ 4</sup>)''σ''<sub>1</sub> \, \sigma_1 (3<sup>^ 2</sup>) = (1<sup>^ 1</sup> + 2<sup>^ 1</sup> + 4<sup>^ 1</sup> + 8<sup>^ 1</sup> + 16<sup>^ 1</sup>)(1<sup>^ 1</sup> + 3<sup>^ 1</sup> + 9<sup>^ 1</sup>) = 31 ·\cdot 13 = 403,}}</math>
{{block<math indent|emdisplay =1.2|text= ''σ''<sup"block" >\sigma^ *</sup>(144) = ''σ''<sup>\sigma^ *</sup>(2<sup>^ 4</sup>)''σ''<sup> \, \sigma^ *</sup>(3<sup>^ 2</sup>) = (1<sup>^ 1</sup> + 16<sup>^ 1</sup>)(1<sup>^ 1</sup> + 9<sup>^ 1</sup>) = 17 ·\cdot 10 = 170.}}</math>
Similarly, we have:
