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A number of the form n^...^_()_(n)n, where Knuth up-arrow notation has been used. The first few Ackermann numbers are 1^1=1, 2^^2=4, and ...

A divisor, also called a factor, of a number n is a number d which divides n (written d|n). For integers, only positive divisors are usually considered, though obviously the ...

Let D be a planar Abelian difference set and t be any divisor of n. Then t is a numerical multiplier of D, where a multiplier is defined as an automorphism alpha of a group G ...

sum_(n=1)^(infty)1/(phi(n)sigma_1(n)) = product_(p prime)(1+sum_(k=1)^(infty)1/(p^(2k)-p^(k-1))) (1) = 1.786576459... (2) (OEIS A093827), where phi(n) is the totient function ...

A dozen dozen, or the square number 144.

Smarandache sequences are any of a number of simply generated integer sequences resembling those considered in published works by Smarandache such as the consecutive number ...

Let m>=3 be an integer and let f(x)=sum_(k=0)^na_kx^(n-k) be an integer polynomial that has at least one real root. Then f(x) has infinitely many prime divisors that are not ...

The classification theorem of finite simple groups, also known as the "enormous theorem," which states that the finite simple groups can be classified completely into 1. ...

A sentential formula that contains at least one free variable (Carnap 1958, p. 24). A sentential variable containing no free variables (i.e., all variables are bound) is ...

Let P(N) denote the number of primes of the form n^2+1 for 1<=n<=N, then P(N)∼0.68641li(N), (1) where li(N) is the logarithmic integral (Shanks 1960, pp. 321-332). Let Q(N) ...