The amicable numbers, also known as friendly numbers, were known to Pythagoras. The distribution of even and odd amicable pairs below 1020, along with some special amicable pairs such as Harshad, happy, Smith, pandigital, and ESD (equal sum of digits) amicable pairs, are discussed. Divisibility and the digital roots of known amicable numbers, along with the prime factors of amicable numbers, are dealt with in detail. Amicable triplets and multiplets, quasi-amicable pairs, and augmented amicable pairs are also covered in this chapter.

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Amicable Numbers

  • Shyam Sunder Gupta

摘要

The amicable numbers, also known as friendly numbers, were known to Pythagoras. The distribution of even and odd amicable pairs below 1020, along with some special amicable pairs such as Harshad, happy, Smith, pandigital, and ESD (equal sum of digits) amicable pairs, are discussed. Divisibility and the digital roots of known amicable numbers, along with the prime factors of amicable numbers, are dealt with in detail. Amicable triplets and multiplets, quasi-amicable pairs, and augmented amicable pairs are also covered in this chapter.