Le Monde puzzle [#1139]

A weekly Monde current mathematical puzzle that reminded me of an earlier one (but was too lazy to check):

The integer n=36 enjoys the property that all the differences between its ordered divisors are also divisors of 36. Find the only 18≤m≤100 that enjoys this property such that all its prime dividers areof multiplicity one. Are there other such m’s?

The run of a brute force R search return 42 as the solution (codegolf welcomed!)

y=z=1:1e5
for(x in y)z[y==x]=!sum(x%%diff((1:x)[!x%%(1:x)]))
y=y[z==1]
for(k in generate_primes(2,max(y)))y=y[!!y%%k^2]

where generate_primes is a primes R function. Increasing the range of y’s to 10⁵ exhibits one further solution, 1806.

2 Responses to “Le Monde puzzle [#1139]”

  1. […] article was first published on R – Xi'an's Og, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here) […]

  2. […] by data_admin [This article was first published on R – Xi’an’s Og, and kindly contributed to R-bloggers]. (You can report issue about the content on this page […]

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