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An n-persistent number is a positive integer k which contains the digits 0, 1, ..., 9 (i.e., is a pandigital number), and for which 2k, ..., nk also share this property. No ...

That part of a positive integer left after all square factors are divided out. For example, the squarefree part of 24=2^3·3 is 6, since 6·2^2=24. For n=1, 2, ..., the first ...

A nonnegative matrix is a real or integer matrix (a)_(ij) for which each matrix element is a nonnegative number, i.e., a_(ij)>=0 for all i, j. Nonnegative matrices are ...

An element B of a ring is nilpotent if there exists a positive integer k for which B^k=0.

The least positive integer m^* with the property that chi(y)=1 whenever y=1 (mod m^*) and (y,m)=1.

A partition is a way of writing an integer n as a sum of positive integers where the order of the addends is not significant, possibly subject to one or more additional ...

Physicists and engineers use the phrase "order of magnitude" to refer to the smallest power of ten needed to represent a quantity. Two quantities A and B which are within ...

The even part Ev(n) of a positive integer n is defined by Ev(n)=2^(b(n)), where b(n) is the exponent of the exact power of 2 dividing n. The values for n=1, 2, ..., are 1, 2, ...

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 ...

The largest cube dividing a positive integer n. For n=1, 2, ..., the first few are 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, ... (OEIS A008834).