On the solutions of .

Weingartner, Andreas

Displaying similar documents to “On the solutions of $σ (n) = σ (n + k)$ .”

Partial sums of powers of prime factors.

De Koninck, Jean-Marie, Luca, Florian (2007)

Journal of Integer Sequences [electronic only]

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On the irrationality of a divisor function series.

Friedlander, John B., Luca, Florian, Stoiciu, Mihai (2007)

Integers

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Square-free Lucas $d$ -pseudoprimes and Carmichael-Lucas numbers

Walter Carlip, Lawrence Somer (2007)

Czechoslovak Mathematical Journal

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Let $d$ be a fixed positive integer. A Lucas $d$ -pseudoprime is a Lucas pseudoprime $N$ for which there exists a Lucas sequence $U (P, Q)$ such that the rank of $N$ in $U (P, Q)$ is exactly $(N - ε (N)) / d$ , where $ε$ is the signature of $U (P, Q)$ . We prove here that all but a finite number of Lucas $d$ -pseudoprimes are square free. We also prove that all but a finite number of Lucas $d$ -pseudoprimes are Carmichael-Lucas numbers.

How to differentiate a number.

Ufnarovski, Victor, Åhlander, Bo (2003)

Journal of Integer Sequences [electronic only]

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GCD of truncated rows in Pascal's triangle.

Kaplan, Gil, Levy, Dan (2004)

Integers

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A new Fibonacci-like sequence of composite numbers.

Vsemirnov, M. (2004)

Journal of Integer Sequences [electronic only]

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The number of representations by sums of squares and triangular numbers.

Lam, Heung Yeung (2007)

Integers

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On the composition factors of a group with the same prime graph as $B_{n} (5)$

Azam Babai, Behrooz Khosravi (2012)

Czechoslovak Mathematical Journal

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Let $G$ be a finite group. The prime graph of $G$ is a graph whose vertex set is the set of prime divisors of $| G |$ and two distinct primes $p$ and $q$ are joined by an edge, whenever $G$ contains an element of order $p q$ . The prime graph of $G$ is denoted by $Γ (G)$ . It is proved that some finite groups are uniquely determined by their prime graph. In this paper, we show that if $G$ is a finite group such that $Γ (G) = Γ (B_{n} (5))$ , where $n \geq 6$ , then $G$ has a unique nonabelian composition factor isomorphic to $B_{n} (5)$ or $C_{n} (5)$ .

Arithmetical characterizations of divisor class groups. II.

Geroldinger, A. (1992)

Acta Mathematica Universitatis Comenianae. New Series

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Displaying similar documents to “On the solutions of σ ( n ) = σ ( n + k ) .”

Displaying similar documents to “On the solutions of $σ (n) = σ (n + k)$ .”