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Omni-MATH / A sequence (a_(n))_(n=1)^(∞) of positive integers satisfies the condition a_(n+1)=a_(n)+τ(n) for all positive integers n where τ(n) is the number of positive integer divisors of n.…

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problem

A sequence (an)n=1∞(a_n)_{n=1}^{\infty} of positive integers satisfies the condition an+1=an+τ(n)a_{n+1} = a_n +\tau (n) for all positive integers nn where τ(n)\tau (n) is the number of positive integer divisors of nn. Determine whether two consecutive terms of this sequence can be perfect squares.
Plain-text mathematical notation (without MathML)
A sequence (a_(n))_(n=1)^(∞) of positive integers satisfies the condition a_(n+1)=a_(n)+τ(n) for all positive integers n where τ(n) is the number of positive integer divisors of n. Determine whether two consecutive terms of this sequence can be perfect squares.
Original LaTeX notation
A sequence $(a_n)_{n=1}^{\infty}$ of positive integers satisfies the condition $a_{n+1} = a_n +\tau (n)$ for all positive integers $n$ where $\tau (n)$ is the number of positive integer divisors of $n$. Determine whether two consecutive terms of this sequence can be perfect squares.

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Source and history

task_id
c28c7d2d-c604-5e9c-b0ff-9e5c0fe1e9f2
task_key
test--c28c7d2d-c604-5e9c-b0ff-9e5c0fe1e9f2
task_revision_id
1
config / split
/ test

Official source

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