Odd Proper Divisors

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The Number of odd proper divisors of 3 p 6 m 2 1 n 3^{p}\cdot6^{m}\cdot21^{n} is :

(p+m+n+1)(n+1) -1 (p+1)(m+1)(n+1) -1 (p+m+n+1)(n+1)-2 (p+m)(m+1)(n+1)-2

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1 solution

Kshitij Dhariwal
Mar 19, 2018

3 p 6 m 2 1 n 3^{p}\cdot6^{m}\cdot21^{n} = 2 m 3 ( p + m + n ) 7 n 2^{m}\cdot3^(p+m+n)\cdot7^{n} Therefore , the required number of proper divisors = numbrer of selections of any number of 3s and 7s [since, for odd divisors 2 must not be selected ] therefore after selection , ( p + m + n + 1 ) ( n + 1 ) 1 \boxed{(p+m+n+1)(n+1)-1}

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