The divisor function at consecutive integers

DOI10.1112/S0025579300010743zbMath0529.10040OpenAlexW2009526696MaRDI QIDQ5896188

D. R. Heath-Brown

Publication date: 1984

Published in: Mathematika (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1112/s0025579300010743

zbMATH Keywords

divisor functionparity problemweighted linear sieve

Mathematics Subject Classification ID

Applications of sieve methods (11N36) Rate of growth of arithmetic functions (11N56)

Related Items (22)

On consecutive k-th power residues ⋮ On locally repeated values of certain arithmetic functions. II ⋮ Non-commutative Noetherian Unique Factorization Domains often have stable range one ⋮ Congruences for arithmetic functions ⋮ Small gaps between primes or almost primes ⋮ Symmetric primes revisited ⋮ Small gaps between three almost primes and almost prime powers ⋮ On the difference of the number of prime divisors of consecutive numbers ⋮ Closed-form calculation of infinite products of Glaisher-type related to Dirichlet series ⋮ Notes on the equation \(d(n)=D(\varphi(n))\) and related inequalities ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Small gaps between almost primes, the parity problem, and some conjectures of Erdős on consecutive integers II. ⋮ Fifteen consecutive integers with exactly four prime factors ⋮ On a Conjecture of Balog ⋮ On the bivariate Erdős–Kac theorem and correlations of the Möbius function ⋮ Unnamed Item ⋮ Landau's problems on primes ⋮ Multiplicative functions on shifted primes ⋮ A tale of two omegas ⋮ On the lcm of the Differences of Eight Primes ⋮ DISTRIBUTION OF THE DIVISOR FUNCTION AT CONSECUTIVE INTEGERS

Cites Work

• A remark on the divisor function d(n)
• The Distribution of Values of the Divisor Function d(n)

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