Documentation

The prime numbers, i.e. A000040.

Tetranacci numbers, i.e. A000078.

Euler up/down numbers: e.g.f. \(\sec(x) + \tan(x)\), i.e. A000111.

Tangent (or "Zag") numbers: e.g.f. \(\tan(x)\), also (up to signs) e.g.f. \(\tanh(x)\), i.e. A000182.

Triangular numbers, i.e. A000217.

The squares: \(a000290(n) = n^2\), i.e. A000290.

Euler (or secant or "Zig") numbers: e.g.f. (even powers only) \(\sec(x) = \frac{1}{\cos(x)}\), i.e. A000364.

Oblong (or promic, pronic, or heteromecic) numbers: \(a002378(n) = n(n+1)\), i.e. A002378.

Length of shortest addition chain for \(n\), i.e. A003313.

Largest squarefree number diving \(n\): the square free kernel of \(n\), \(\text{rad}(n)\), radical of \(n\), i.e. A007947.

Digital sum of \(n\), i.e. A007953.

Irregular triangle in which first row is \(1\), \(n\)-th row \((n > 1)\) lists distinct prime factors of \(n\), i.e. A027748.

See distinctPrimeFactors.

Numbers that are sums of consecutive squares, i.e. A034705.

See also a000290 and squares.

Smallest number whose sum of digits is \(n\), i.e. A051885.

See also a007953 and digitSum.

Number of divisors of \(n\) that are smaller than \(\sqrt{n}\), i.e. A056924.

\(a056924(n) = N(4n)\) from Project Euler Problem 174: Hollow Square Laminae II.

\(a060735(1) = 1\), \(a060735(2) = 2\); thereafter, \(a060735(n)\) is the smallest number \(m\) not yet in the sequence such that every prime that divides \(a(n-1)\) also divides \(m\), i.e. A060735.

See a007947.

\(a076314(n) = \lfloor \frac{n}{10} \rfloor + (n \bmod 10)\), i.e. A0076314.

Numbers of the form \(p^{q}q^{p}\), with distinct primes \(p\) and \(q\), i.e. A082949.

Numbers \(k\) such that \(3k^2 + 3k + 1\) is prime, i.e. A111251.

The number of base-10 bouncy numbers below \(10^{n}\), i.e. A204692.

Number of integer pairs \((x,y,)\) such that \(0 < x < y \leq n\) and \(xy \leq n\), i.e. A211264.

See a007953.

The distinct prime factors of a given number.

>>> distinctPrimeFactors 504
2 :| [3,7]

See also a007947 and a027748.

See a000290.

See a000217.