Some Aspects of Certain Form of Near Perfect Numbers

Bhabesh Das; Helen K. Saikia

doi:doi:10.11648/j.dmath.20170203.12

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Some Aspects of Certain Form of Near Perfect Numbers

Bhabesh Das, Helen K. Saikia

Published in International Journal of Discrete Mathematics (Volume 2, Issue 3)

Received: 29 January 2017 Accepted: 7 March 2017 Published: 24 March 2017

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Abstract

It is well known that a positive integer n is said to be near perfect number, if σ(n) = 2n+d where d is a proper divisor of n and function σ(n) is the sum of all positive divisors of n In this paper, we discuss some results concerning with near perfect numbers from known near perfect numbers.

Published in	International Journal of Discrete Mathematics (Volume 2, Issue 3)
DOI	10.11648/j.dmath.20170203.12
Page(s)	64-67
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2017. Published by Science Publishing Group

Keywords

Divisor Function, Mersenne Prime, Fermat Prime, Perfect Number, Near Perfect Number

References

[1]	T. M. Apostol, Introduction to Analytic Number Theory, Springer Verlag, New York, 1976.
[2]	David M. Burton, Elementary Number Theory, Tata McGraw-Hill, Sixth Edition, 2007.
[3]	R. D. Carmichael, Multiply perfect numbers of three different primes, Ann. Math., 8 (1) (1906): 49–56.
[4]	R. D. Carmichael, Multiply perfect numbers of four different primes, Ann. Math., 8 (4) (1907): 149–158.
[5]	B. Das, H. K. Saikia, Identities for Near and Deficient Hyperperfect Numbers, Indian J. Num. Theory, 3 (2016), 124-134.
[6]	B. Das, H. K. Saikia, On Near 3−Perfect Numbers, Sohag J. Math., 4 (1) (2017), 1- 5.
[7]	L. E. Dickson, History of the theory of numbers, Vol. I: Divisibility and primality, Chelsea Publishing Co., New York, 1966.
[8]	Euclid, Elements, Book IX, Prop. 36.
[9]	L. Euler, Opera postuma 1 (1862), p. 14-15.
[10]	P. Pollack, V. Shevelev, On perfect and near perfect numbers, J. Num. Theory, 132 (2012), 3037–3046.
[11]	D. Surynarayana, Super perfect numbers, Elem. Math., 24 (1969), 16 -17.
[12]	J. Westlund, Note on multiply perfect numbers. Ann. Math., 2nd Ser., 2 (1) (1900), 172–174.
[13]	D. Minoli, R. Bear, Hyperperfect numbers, Pi Mu Epsilon J., Vol. 6 (1975), 153-157.
[14]	Great Internet Mersenne Prime Search (GIMPS), http://www.Mersenne.org/.

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Bhabesh Das, Helen K. Saikia. (2017). Some Aspects of Certain Form of Near Perfect Numbers. International Journal of Discrete Mathematics, 2(3), 64-67. https://doi.org/10.11648/j.dmath.20170203.12

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ACS Style

Bhabesh Das; Helen K. Saikia. Some Aspects of Certain Form of Near Perfect Numbers. Int. J. Discrete Math. 2017, 2(3), 64-67. doi: 10.11648/j.dmath.20170203.12

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AMA Style

Bhabesh Das, Helen K. Saikia. Some Aspects of Certain Form of Near Perfect Numbers. Int J Discrete Math. 2017;2(3):64-67. doi: 10.11648/j.dmath.20170203.12

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@article{10.11648/j.dmath.20170203.12,
  author = {Bhabesh Das and Helen K. Saikia},
  title = {Some Aspects of Certain Form of Near Perfect Numbers},
  journal = {International Journal of Discrete Mathematics},
  volume = {2},
  number = {3},
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  doi = {10.11648/j.dmath.20170203.12},
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  abstract = {It is well known that a positive integer n is said to be near perfect number, if σ(n) = 2n+d where d is a proper divisor of n and function σ(n) is the sum of all positive divisors of n In this paper, we discuss some results concerning with near perfect numbers from known near perfect numbers.},
 year = {2017}
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T1  - Some Aspects of Certain Form of Near Perfect Numbers
AU  - Bhabesh Das
AU  - Helen K. Saikia
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PY  - 2017
N1  - https://doi.org/10.11648/j.dmath.20170203.12
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AB  - It is well known that a positive integer n is said to be near perfect number, if σ(n) = 2n+d where d is a proper divisor of n and function σ(n) is the sum of all positive divisors of n In this paper, we discuss some results concerning with near perfect numbers from known near perfect numbers.
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Author Information

Bhabesh Das

Department of Mathematics, B. P. C. College, Nagarbera, Assam, India
Helen K. Saikia

Department of Mathematics, Gauhati University, Guwahati, Assam, India

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Plain Text BibTeX RIS

APA Style

Bhabesh Das, Helen K. Saikia. (2017). Some Aspects of Certain Form of Near Perfect Numbers. International Journal of Discrete Mathematics, 2(3), 64-67. https://doi.org/10.11648/j.dmath.20170203.12

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ACS Style

Bhabesh Das; Helen K. Saikia. Some Aspects of Certain Form of Near Perfect Numbers. Int. J. Discrete Math. 2017, 2(3), 64-67. doi: 10.11648/j.dmath.20170203.12

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AMA Style

Bhabesh Das, Helen K. Saikia. Some Aspects of Certain Form of Near Perfect Numbers. Int J Discrete Math. 2017;2(3):64-67. doi: 10.11648/j.dmath.20170203.12

Copy | Download

@article{10.11648/j.dmath.20170203.12,
  author = {Bhabesh Das and Helen K. Saikia},
  title = {Some Aspects of Certain Form of Near Perfect Numbers},
  journal = {International Journal of Discrete Mathematics},
  volume = {2},
  number = {3},
  pages = {64-67},
  doi = {10.11648/j.dmath.20170203.12},
  url = {https://doi.org/10.11648/j.dmath.20170203.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.dmath.20170203.12},
  abstract = {It is well known that a positive integer n is said to be near perfect number, if σ(n) = 2n+d where d is a proper divisor of n and function σ(n) is the sum of all positive divisors of n In this paper, we discuss some results concerning with near perfect numbers from known near perfect numbers.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Some Aspects of Certain Form of Near Perfect Numbers
AU  - Bhabesh Das
AU  - Helen K. Saikia
Y1  - 2017/03/24
PY  - 2017
N1  - https://doi.org/10.11648/j.dmath.20170203.12
DO  - 10.11648/j.dmath.20170203.12
T2  - International Journal of Discrete Mathematics
JF  - International Journal of Discrete Mathematics
JO  - International Journal of Discrete Mathematics
SP  - 64
EP  - 67
PB  - Science Publishing Group
SN  - 2578-9252
UR  - https://doi.org/10.11648/j.dmath.20170203.12
AB  - It is well known that a positive integer n is said to be near perfect number, if σ(n) = 2n+d where d is a proper divisor of n and function σ(n) is the sum of all positive divisors of n In this paper, we discuss some results concerning with near perfect numbers from known near perfect numbers.
VL  - 2
IS  - 3
ER  -

Copy | Download