Powerful numbers in \((1^k +1)(2^k+1) \cdots (n^k +1)\)

DOI10.1016/j.jnt.2012.05.025zbMath1255.11001OpenAlexW2312861637MaRDI QIDQ452395

Wen Peng Zhang, Ting-Ting Wang

Publication date: 21 September 2012

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2012.05.025

zbMATH Keywords

powerful numbershifted powerexplicit prime number theorem

Mathematics Subject Classification ID

Arithmetic functions; related numbers; inversion formulas (11A25) Distribution of primes (11N05)

Related Items (8)

On the products \((1^{3}+q^{3})(2^{3}+q^{3})\cdots (n^{3}+q^{3})\) ⋮ On the Occurrence of Perfect Squares Among Values of Certain Polynomial Products ⋮ On the products \((1^\ell + 1)(2^\ell + 1)\cdots(n^\ell + 1)\). II ⋮ Products of consecutive values of some quartic polynomials ⋮ Numbers of the form \((1^{\ell}+q^{\ell})(2^{\ell}+q^{\ell})\cdots(n^{\ell}+q^\ell)\) that are not powerful ⋮ On the products \((1^\ell +1)(2^\ell +1)\cdots (n^\ell +1)\) ⋮ Prime powers dividing products of consecutive integer values of \(x^{2^n}+1\) ⋮ Polynomial products modulo primes and applications

Cites Work

• Arithmetical properties of a sequence arising from an arctangent sum
• Squares in \((1^2+1)\dots(n^2+1)\)
• A note on the products \((1^\mu +1)(2^\mu +1)\dots (n^\mu +1)\)
• The large sieve
• The 𝑘^{𝑡ℎ} prime is greater than 𝑘(ln𝑘+lnln𝑘-1) for 𝑘≥2
• Powerful Numbers

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