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A number n is called an Egyptian number if it is the sum of the denominators in some unit fraction representation of a positive whole number not consisting entirely of 1s. ...

A Proth number is a number of the form N=k·2^n+1 for odd k, n a positive integer, and 2^n>k. The 2^n>k condition is needed since otherwise, every odd number >1 would be a ...

The number of alternating permutations for n elements is sometimes called an Euler zigzag number. Denote the number of alternating permutations on n elements for which the ...

The Gelfond-Schneider constant is sometimes known as the Hilbert number. Flannery and Flannery (2000, p. 35) define a Hilbert number as a positive integer of the form n=4k+1 ...

A number x in which the first n decimal digits of the fractional part frac(x) sum to 666 is known as an evil number (Pegg and Lomont 2004). However, the term "evil" is also ...

A "weird number" is a number that is abundant (i.e., the sum of proper divisors is greater than the number) without being pseudoperfect (i.e., no subset of the proper ...

A number is said to be pandigital if it contains each of the digits from 0 to 9 (and whose leading digit must be nonzero). However, "zeroless" pandigital quantities contain ...

Consider an n-digit number k. Square it and add the right n digits to the left n or n-1 digits. If the resultant sum is k, then k is called a Kaprekar number. For example, 9 ...

A Smith number is a composite number the sum of whose digits is the sum of the digits of its prime factors (excluding 1). (The primes are excluded since they trivially ...

A Belphegor number (also known as a Beelphegor number or a beastly palindromic prime) is a palindromic number of the form 1(0...)666(0...)1. Numbers of this form are named ...