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Omni-MATH / A triple of positive integers (a,b,c) is tasty if lcm(a,b,c)∣a+b+c−1 and a<b<c. Find the sum of a+b+c across all tasty triples.

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problem

A triple of positive integers (a,b,c)(a, b, c) is tasty if lcm(a,b,c)∣a+b+c−1\operatorname{lcm}(a, b, c) \mid a+b+c-1 and a<b<ca<b<c. Find the sum of a+b+ca+b+c across all tasty triples.
Plain-text mathematical notation (without MathML)
A triple of positive integers (a,b,c) is tasty if lcm(a,b,c)∣a+b+c−1 and a<b<c. Find the sum of a+b+c across all tasty triples.
Original LaTeX notation
A triple of positive integers $(a, b, c)$ is tasty if $\operatorname{lcm}(a, b, c) \mid a+b+c-1$ and $a<b<c$. Find the sum of $a+b+c$ across all tasty triples.

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Source and history

task_id
50814f1a-8e18-5172-a7b0-eacda8e8fa13
task_key
test--50814f1a-8e18-5172-a7b0-eacda8e8fa13
task_revision_id
1
config / split
/ test

Official source

initial import