Factorion, that is, positive integers that are equal to the sum of the factorials of their digits like 1, 2, 145, and 40585, along with amicable factorion and magic factorion, are discussed in this chapter. The methodology to compute the number of digits and trailing zeros in a factorial is given. The maximum number of iterations required to reach factorion, amicable factorion, and magic factorion is tabulated. Using factorial digits, the possibility of drawing amazing shapes like triangles, rhombuses, hexagons, octagons, etc. is discussed. Various kinds of factorials like half, double, multi-, hyper, and super factorials and sub-factorials are covered, along with some curiosities like 372973, the only number that is one less than the sum of the factorials of their digits. Factorial primes, along with some curiosities with prime counting functions, are covered in this chapter.

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Fascinating Factorials

  • Shyam Sunder Gupta

摘要

Factorion, that is, positive integers that are equal to the sum of the factorials of their digits like 1, 2, 145, and 40585, along with amicable factorion and magic factorion, are discussed in this chapter. The methodology to compute the number of digits and trailing zeros in a factorial is given. The maximum number of iterations required to reach factorion, amicable factorion, and magic factorion is tabulated. Using factorial digits, the possibility of drawing amazing shapes like triangles, rhombuses, hexagons, octagons, etc. is discussed. Various kinds of factorials like half, double, multi-, hyper, and super factorials and sub-factorials are covered, along with some curiosities like 372973, the only number that is one less than the sum of the factorials of their digits. Factorial primes, along with some curiosities with prime counting functions, are covered in this chapter.