Discrete Mathematics with Applications 4th Edition

Published by Cengage Learning
ISBN 10: 0-49539-132-8
ISBN 13: 978-0-49539-132-6

Chapter 7 - Functions - Exercise Set 7.1 - Page 394: 9

Answer

$a-1\\ b-24 \\ c-18 \\ d-6 \\ e-39 \\ f-32 \\ $

Work Step by Step

$S:\mathbb{Z}^+\rightarrow \mathbb{Z}^+ \\ S(n)=the\,\,sum\,of\,the\,positive\,divisors\,of\,n.\\ divisors\,of\,1 : 1\\ S(1)=1 \\ divisors\,of\,15 : 1,3,5,15\\ S(15)=1+3+5+15=24 \\ divisors\,of\,17 : 1,17\\ S(17)=1+17=18 \\ divisors\,of\,5 : 1,5\\ S(5)=1+5=6 \\ divisors\,of\,18 : 1,2,3,6,9,18\\ S(18)=1+2+3+6+9+18=39 \\ divisors\,of\,21 : 1,3,7,21\\ S(21)=1+3+7+21=32 \\ $
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