title: A conjecture of De Koninck regarding particular square values of the sum of divisors function

authors: Broughan, Kevin A.

subjects: Science & Technology

abstract: We study integers n > 1 satisfying the relation σ(n) = γ(n)², where σ(n) and γ(n) are the sum of divisors and the product of distinct primes dividing n, respectively. If the prime dividing a solution n is congruent to 3 modulo 8 then it must be greater than 41, and every solution is divisible by at least the fourth power of an odd prime. Moreover at least 2/5 of the exponents a of the primes dividing any solution have the property that a + 1 is a prime power. Lastly we prove that the number of solutions up to x > 1 is at most x¹/⁶⁺є, for any є > 0 and all x > xє.

text: A conjecture of De Koninck regarding particular square values of the sum of divisors function We study integers n > 1 satisfying the relation σ(n) = γ(n)², where σ(n) and γ(n) are the sum of divisors and the product of distinct primes dividing n, respectively. If the prime dividing a solution n is congruent to 3 modulo 8 then it must be greater than 41, and every solution is divisible by at least the fourth power of an odd prime. Moreover at least 2/5 of the exponents a of the primes dividing any solution have the property that a + 1 is a prime power. Lastly we prove that the number of solutions up to x > 1 is at most x¹/⁶⁺є, for any є > 0 and all x > xє.

year: 2014

title: When it's not safe to be me: employee authenticity mediates the effect of perceived manager psychopathy on employee well-being.

authors: Sutton, Anna

subjects: Authenticity

abstract: BACKGROUND: Psychopathy in managers is often measured on global scales and associated with detrimental outcomes for subordinates, such as bullying and reduced well-being. Yet some features of psychopathy, like boldness, appear to have beneficial outcomes. Using the triarchic model of psychopathy, we differentiate between adaptive and maladaptive traits in managers and model their effects on employee engagement and burnout. In addition, we test the extent to which authenticity, known to ameliorate the effect of some negative experiences on well-being, might mediate the influence of managers' perceived psychopathic traits on employee well-being. METHODS: In a two-wave study, full-time employees (N = 246) reported on their manager's psychopathic traits (boldness, meanness, disinhibition), their own authenticity and, six weeks later, their engagement and burnout. RESULTS: In support of our hypotheses, manager boldness enhanced engagement and reduced burnout while meanness and disinhibition reduced engagement and increased burnout. Additionally, employee authenticity was a partial mediator of the effect of managerial psychopathy on engagement and burnout. CONCLUSIONS: Perceived psychopathic traits in managers have the potential to influence whether employees feel able to be their authentic selves at work, which consequently affects their well-being. A work culture that values authenticity can directly improve well-being and help employees to deal with managerial behaviour that stems from maladaptive psychopathic traits. We also highlight the importance of discriminating between constituent psychopathic traits to identify the potentially adaptive nature of the boldness element of psychopathy.

text: When it's not safe to be me: employee authenticity mediates the effect of perceived manager psychopathy on employee well-being. BACKGROUND: Psychopathy in managers is often measured on global scales and associated with detrimental outcomes for subordinates, such as bullying and reduced well-being. Yet some features of psychopathy, like boldness, appear to have beneficial outcomes. Using the triarchic model of psychopathy, we differentiate between adaptive and maladaptive traits in managers and model their effects on employee engagement and burnout. In addition, we test the extent to which authenticity, known to ameliorate the effect of some negative experiences on well-being, might mediate the influence of managers' perceived psychopathic traits on employee well-being. METHODS: In a two-wave study, full-time employees (N = 246) reported on their manager's psychopathic traits (boldness, meanness, disinhibition), their own authenticity and, six weeks later, their engagement and burnout. RESULTS: In support of our hypotheses, manager boldness enhanced engagement and reduced burnout while meanness and disinhibition reduced engagement and increased burnout. Additionally, employee authenticity was a partial mediator of the effect of managerial psychopathy on engagement and burnout. CONCLUSIONS: Perceived psychopathic traits in managers have the potential to influence whether employees feel able to be their authentic selves at work, which consequently affects their well-being. A work culture that values authenticity can directly improve well-being and help employees to deal with managerial behaviour that stems from maladaptive psychopathic traits. We also highlight the importance of discriminating between constituent psychopathic traits to identify the potentially adaptive nature of the boldness element of psychopathy.

year: 2023-10-09

title: The development of guidelines for indigenous research ethics in Aotearoa/New Zealand.

authors: Hudson, Maui

abstract: The development of Indigenous frameworks for research ethics has been a key component of progressing Indigenous aspirations for research around the world. They have provided a focal point for challenging approaches to research that prioritise non-Indigenous methods and values, and allow non-Indigenous researchers to claim expert status over Indigenous peoples, places and knowledges. The theme of self-determination underpins contemporary approaches to Indigenous development and the repositioning of state-Indigenous nation relationships. This paper describes the background, development, and implementation by Māori communities and researchers of an Indigenous ethical framework in Aotearoa/New Zealand.

text: The development of guidelines for indigenous research ethics in Aotearoa/New Zealand. The development of Indigenous frameworks for research ethics has been a key component of progressing Indigenous aspirations for research around the world. They have provided a focal point for challenging approaches to research that prioritise non-Indigenous methods and values, and allow non-Indigenous researchers to claim expert status over Indigenous peoples, places and knowledges. The theme of self-determination underpins contemporary approaches to Indigenous development and the repositioning of state-Indigenous nation relationships. This paper describes the background, development, and implementation by Māori communities and researchers of an Indigenous ethical framework in Aotearoa/New Zealand.

year: 2016