A Note On Perfect Totient Numbers

被引：0
|
作者：
Deng, Moujie [1 ]
机构：
[1] Hainan Univ, Coll Informat Sci & Technol, Dept Appl Math, Haikou 570228, Peoples R China
来源：
JOURNAL OF INTEGER SEQUENCES | 2009年 / 12卷 / 06期
关键词：
totient; perfect totient number; diophantine equation;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this note we prove that there are no perfect totient numbers of the form 3(k) p, k >= 4, where s = 2(a)3(b) + 1, r = 2(c)3(d) s + 1, q = 2(e)3(f) r + 1, and p = 2(g)3(h) q + 1 are primes with a, c, e, g >= 1, and b, d, f, h >= 0.
引用
收藏
页数：8
相关论文
共 50 条
  • [1] PERFECT TOTIENT NUMBERS
    MOHAN, AL
    SURYANARAYANA, D
    [J]. LECTURE NOTES IN MATHEMATICS, 1982, 938 : 101 - 105
  • [2] An analog of perfect numbers involving the unitary totient function
    Yamada, Tomohiro
    [J]. JOURNAL OF NUMBER THEORY, 2020, 209 : 246 - 266
  • [3] A NOTE ON ODD PERFECT NUMBERS
    Dris, Jose Arnaldo B.
    Luca, Florian
    [J]. FIBONACCI QUARTERLY, 2016, 54 (04): : 291 - 295
  • [4] Note on multiply perfect numbers
    Carmichael, RD
    [J]. ANNALS OF MATHEMATICS, 1905, 7 : 153 - 154
  • [5] Note on multiply perfect numbers
    Westlund, J
    [J]. ANNALS OF MATHEMATICS, 1901, 3 : 161 - 163
  • [6] NOTE ON ODD PERFECT NUMBERS
    RAO, DR
    [J]. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES INDIA SECTION A-PHYSICAL SCIENCES, 1972, 42 : 170 - 170
  • [7] Note on multiply perfect numbers
    Westlund, J
    [J]. ANNALS OF MATHEMATICS, 1900, 2 (01) : 172 - 174
  • [8] ON SPARSELY TOTIENT NUMBERS
    HARMAN, G
    [J]. GLASGOW MATHEMATICAL JOURNAL, 1991, 33 : 349 - 358
  • [9] On super totient numbers and super totient labelings of graphs
    Harrington, Joshua
    Wong, Tony W. H.
    [J]. DISCRETE MATHEMATICS, 2020, 343 (02)
  • [10] ON SPARSELY TOTIENT NUMBERS
    MASSER, DW
    SHIU, P
    [J]. PACIFIC JOURNAL OF MATHEMATICS, 1986, 121 (02) : 407 - 426
12345