S-N-S-2-0-2-1-2-13-7-0-7-1-7-15-11-0-11-1-11-100-determinate-the-sum-of-positive-divisors-of-S-

Question Number 124696 by mathocean1 last updated on 05/Dec/20

S \in N .

S = (2^{0} \times 2^{1} \times \dots \times 2^{13}) (7^{0} \times 7^{1} \times \dots \times 7^{15}) (11^{0} \times 11^{1} \times \dots \times 11^{100})

d e t e r m i n a t e t h e s u m o f p o s i t i v e

d i v i s o r s o f S .

Commented by mr W last updated on 05/Dec/20

s e e Q 124332

S = 2^{0 + 1 + 2 + \dots + 13} \times 7^{0 + 1 + 2 + \dots + 15} \times 11^{0 + 1 + 2 + \dots + 100}

= 2^{91} \times 7^{120} \times 11^{5050}

s u m o f a l l d i v i s o r s o f S i s

\frac{(2^{92} - 1) (7^{121} - 1) (11^{5051} - 1)}{(2 - 1) (7 - 1) (11 - 1)}

= \frac{(2^{92} - 1) (7^{121} - 1) (11^{5051} - 1)}{60}

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