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The reversal of a positive integer abc...z is z...cba. The reversal of a positive integer n is implemented in the Wolfram Language as IntegerReverse[n]. A positive integer ...

The number of ways of picking k unordered outcomes from n possibilities. Also known as the binomial coefficient or choice number and read "n choose k," _nC_k=(n; ...

The series producing Brun's constant converges even if there are an infinite number of twin primes, first proved by Brun (1919).

A number n satisfies the Carmichael condition iff (p-1)|(n/p-1) for all prime divisors p of n. This is equivalent to the condition (p-1)|(n-1) for all prime divisors p of n.

The maximum cardinal number of a collection of subsets of a t-element set T, none of which contains another, is the binomial coefficient (t; |_t/2_|), where |_x_| is the ...

A random number which lies within a specified range (which can, without loss of generality, be taken as [0, 1]), with a uniform distribution.

A number is said to be biquadratefree (or quarticfree) if its prime factorization contains no quadrupled factors. All primes and prime powers p^n with n<=3 are therefore ...

A centered triangular number is a centered polygonal number consisting of a central dot with three dots around it, and then additional dots in the gaps between adjacent dots. ...

A polygonal number of the form N_n=n(7n-5)/2, also called an enneagonal number. The first few are 1, 9, 24, 46, 75, 111, 154, 204, ... (OEIS A001106). The generating function ...

Given an integer e>=2, the Payam number E_+/-(e) is the smallest positive odd integer k such that for every positive integer n, the number k·2^n+/-1 is not divisible by any ...