Find-four-positive-integers-each-not-exceeding-70000-and-each-having-more-than-100-divisors-

Question Number 200200 by Fridunatjan08 last updated on 16/Nov/23

F i n d f o u r p o s i t i v e i n t e g e r s,

e a c h n o t e x c e e d i n g 70000 a n d

e a c h h a v i n g m o r e t h a n 100

d i v i s o r s .

Answered by mr W last updated on 16/Nov/23

e x a m p l e s :

50400 h a s 108 d i v i s o r s

55440 h a s 120 d i v i s o r s

60480 h a s 112 d i v i s o r s

65520 h a s 120 d i v i s o r s

69300 h a s 108 d i v i s o r s

\dots \dots

Commented by mr W last updated on 17/Nov/23

s e e a l s o e x p l a n a t i o n f r o m MM 42 s i r

You can't use 'macro parameter character #' in math mode

Commented by Fridunatjan08 last updated on 16/Nov/23

b u t h o w t o f i n d t h e s e n u m b e r s ?

Commented by mr W last updated on 17/Nov/23

t h e n u m b e r c a n b e e x p r e s s e d a s

2^{a} \times 3^{b} \times 5^{c} \times 7^{d} \times 11^{e} \times \dots

n o w y o u s e l e c t a, b, c, d, e, \dots s u c h t h a t

2^{a} \times 3^{b} \times 5^{c} \times 7^{d} \times 11^{e} \times \dots < 70000 a n d

(a + 1) (b + 1) (c + 1) (d + 1) (e + 1) \dots > 100

w e m u s t “ e r r o r a n d {t r y}^{″}!

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