Wyniki wyszukiwania - BazTech

Ograniczanie wyników

3 Commentationes Mathematicae

Znaleziono wyników: 3

Liczba wyników na stronie

Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

Generalized perfect numbers

Shukla D. P., Yadav S.

Commentationes Mathematicae

2013

Vol 53, No. 1

61--72

In this paper a modified form of perfect numbers called (p, q)+ perfect numbers and their properties with examples have been discussed. Further properties of σ+ arithmetical function have been discussed and on its basis a modified form of perfect number called (p, q)+ super perfect numbers have been discussed. A modified form of perfect number called (p, 0)-perfect and their characterization has been studied. In the end of this paper almost super perfect numbers have been introduced.

Composition of arithmetical functions with generalization of perfect and related numbers

Shukla D. P., Yadav S.

Commentationes Mathematicae

2012

Vol. 52, [Z] 2

153--170

In this paper we have studied the deficient and abundent numbers connected with the composition of φ,φ*, σ,σ* and ψ arithmetical functions , where φ is the Euler totient, φ* is the unitary totient, σ is the sum of divisors, σ* is the unitary sum of divisors and ip is the Dedekind function. In 1988, J. Sandor conjectured that ψ(φ(m))≥m, for all odd m and proved that this conjecture is equivalent to ψ(φ(m))≥m/2 for all m. Here we have studied this equivalent conjecture. Further, a necessary and sufficient conditions of primitivity for unitary r-deficient numbers and unitary totient r-deficient numbers have been obtained . Finally, we have discussed the generalization of perfect numbers for an arithmetical function Eα.

On Unitary Analogue of f_g-perfect numbers and Ψ_s-perfect numbers

Shukla D. P., Pandey S.

Commentationes Mathematicae

2011

Vol. 51, [Z] 2

141-153

In this paper unitary analogue of f_g-Perfect numbers and some properties of Dedekind's function and all the Ψ-perfect numbers have been discussed.