Some of the special numbers, like autobiographical numbers, Harshad numbers, parasite numbers, polydivisible numbers, and Ramanujan numbers, are covered in this chapter. Two approaches have been described for finding autobiographical numbers. Harshad numbers defined by Indian recreational mathematician D. R. Kaprekar have been discussed, covering consecutive Harshad numbers, multiple Harshad numbers, and the distribution of Harshad numbers. Three simple methods have been explained for finding true parasite numbers. All thirty-six parasite numbers, including eight true parasite numbers, have been listed. Reverse parasite numbers have also been dealt with. The methodology to compute the only polydivisible pandigital number 3816547290 is explained. The number of polydivisible numbers, along with the smallest and largest polydivisible numbers with n digits, is tabulated. The famous number 1729, also called the Ramanujan number or the Hardy-Ramanujan number, along with interesting observations, has been discussed. Ramanujan triples and quadruples, Taxicab numbers, and Cabtaxi numbers are also covered in this chapter.

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On Some Special Numbers

  • Shyam Sunder Gupta

摘要

Some of the special numbers, like autobiographical numbers, Harshad numbers, parasite numbers, polydivisible numbers, and Ramanujan numbers, are covered in this chapter. Two approaches have been described for finding autobiographical numbers. Harshad numbers defined by Indian recreational mathematician D. R. Kaprekar have been discussed, covering consecutive Harshad numbers, multiple Harshad numbers, and the distribution of Harshad numbers. Three simple methods have been explained for finding true parasite numbers. All thirty-six parasite numbers, including eight true parasite numbers, have been listed. Reverse parasite numbers have also been dealt with. The methodology to compute the only polydivisible pandigital number 3816547290 is explained. The number of polydivisible numbers, along with the smallest and largest polydivisible numbers with n digits, is tabulated. The famous number 1729, also called the Ramanujan number or the Hardy-Ramanujan number, along with interesting observations, has been discussed. Ramanujan triples and quadruples, Taxicab numbers, and Cabtaxi numbers are also covered in this chapter.