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The Racah W-coefficients, sometimes simply called the Racah coefficients (Shore and Menzel 1968, p. 279), are quantities introduced by Racah (1942) that are related to the ...

A number n is called wasteful if the number of digits in the prime factorization of n (including powers) uses more digits than the number of digits in n. The first few ...

By way of analogy with the eban numbers, aban numbers are defined as numbers whose English names do not contain the letter "a" (i.e., "a" is banned). Note that this ...

An Achilles number is a positive integer that is powerful (in the sense that each prime factor occurs with exponent greater than one) but imperfect (in the sense that the ...

A number which does not divide another exactly. For instance, 4 and 5 are aliquant divisors of 6. A number which is not an aliquant divisor (i.e., one that does divide ...

If an aliquot sequence {s^0(n),s(n),s^2(n),...} for a given n is bounded, it either ends at s(1)=0 or becomes periodic. If the sequence is periodic (or eventually periodic), ...

The sequence whose definition is: "t is the first, fourth, eleventh, ... letter of this sentence." The first few values are 1, 4, 11, 16, 24, 29, 33, 35, 39, ... (OEIS ...

A pair of numbers m and n such that sigma(m)=sigma(n)=m+n-1, where sigma(m) is the divisor function. Beck and Najar (1977) found 11 augmented amicable pairs.

A pair of positive integers (a_1,a_2) such that the equations a_1+a_2x=sigma(a_1)=sigma(a_2)(x+1) (1) have a positive integer solution x, where sigma(n) is the divisor ...

The conjecture proposed by Catalan in 1888 and extended by E. Dickson that each aliquot sequence ends in a prime, a perfect number, or a set of sociable numbers. The ...